results for au:Sun_B in:math

- Dec 18 2017 math.RT arXiv:1712.05552v1Let $\mathbf G$ be a complex orthogonal or complex symplectic group, and let $G$ be a real form of $\mathbf G$, namely $G$ is a real orthogonal group, a real symplectic group, a quaternionic orthogonal group, or a quaternionic symplectic group. For a fixed parity $\mathbb p\in \mathbb Z/2\mathbb Z$, we define a set $\mathrm{Nil}^{\mathbb p}_{\mathbf G}(\mathfrak g)$ of nilpotent $\mathbf G$-orbits in $\mathfrak g$ (the Lie algebra of $\mathbf G$). When $\mathbb p$ is the parity of the dimension of the standard module of $\mathbf G$, this is the set of the stably trivial special nilpotent orbits, which includes all rigid special nilpotent orbits. For each $\mathcal O \in \mathrm{Nil}^{\mathbb p}_{\mathbf G}(\mathfrak g)$, we construct all unipotent representations of $G$ (or its metaplectic cover when $G$ is a real symplectic group and $\mathbb p$ is odd) attached to $\mathcal O$ via the method of theta lifting and show in particular that they are unitary.
- Sep 19 2017 math.NT arXiv:1709.05762v1Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of "ordinary $p$-adic automorphic forms along a parabolic subgroup" and show that they interpret all classical ordinary automorphic forms.
- Sep 19 2017 math.RT arXiv:1709.05759v1We relate poles of local Godement-Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to $GL_n(F)$ of generic irreducible representations of $GL_n(F)$, where $F$ is an arbitrary local field.
- A battery swapping and charging station (BSCS) is an energy refueling station, where i) electric vehicles (EVs) with depleted batteries (DBs) can swap their DBs for fully-charged ones, and ii) the swapped DBs are then charged until they are fully-charged. Successful deployment of a BSCS system necessitates a careful planning of swapping- and charging-related infrastructures, and thus a comprehensive performance evaluation of the BSCS is becoming crucial. This paper studies such a performance evaluation problem with a novel mixed queueing network (MQN) model and validates this model with extensive numerical simulation. We adopt the EVs' blocking probability as our quality-of-service measure and focus on studying the impact of the key parameters of the BSCS (e.g., the numbers of parking spaces, swapping islands, chargers, and batteries) on the blocking probability. We prove a necessary and sufficient condition for showing the ergodicity of the MQN when the number of batteries approaches infinity, and further prove that the blocking probability has two different types of asymptotic behaviors. Meanwhile, for each type of asymptotic behavior, we analytically derive the asymptotic lower bound of the blocking probability.
- Jul 18 2017 math.GR arXiv:1707.04587v3We give a dynamical characterization of acylindrically hyperbolic groups. As an application, we prove that non-elementary convergence groups are acylindrically hyperbolic.
- Mar 21 2017 math.RT arXiv:1703.06238v1Let $\rk$ be a local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $\GL_{2n}(\rk)$. We prove that for all but countably many characters $\chi$ of $\GL_n(\rk)\times \GL_n(\rk)$, the space of $\chi$-equivariant (continuous in the archimedean case) linear functionals on $\pi$ is at most one dimensional. Using this, we prove the uniqueness of twisted Shalika models.
- Dec 02 2016 math.GR arXiv:1612.00134v3We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.
- Nov 22 2016 math.RT arXiv:1611.06298v1An "automatic continuity" question has naturally occurred since Roger Howe established the local theta correspondence over $\mathbb R$: does the algebraic version of local theta correspondence over $\mathbb R$ agrees with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.
- In this paper, we consider two particular binomial sums \beginalign* \sum_k=0^n-1(20k^2+8k+1)\binom2kk^5 (-4096)^n-k-1 \endalign* and \beginalign* \sum_k=0^n-1(120k^2+34k+3)\binom2kk^4\binom4k2k 65536^n-k-1, \endalign* which are inspired by two series for $\frac{1}{\pi^2}$ obtained by Guillera. We consider their divisibility properties and prove that they are divisible by $2n^2 \binom{2n}{n}^2$ for all integer $n\geq 2$. These divisibility properties are stronger than those divisibility results found by He, who proved the above two sums are divisible by $2n \binom{2n}{n}$ with the WZ-method.
- Jun 28 2016 math.CO arXiv:1606.08153v1Recently, Z. W. Sun introduced a sequence $(S_n)_{n\geq 0}$, where $S_n=\frac{\binom{6n}{3n} \binom{3n}{n}}{2(2n+1)\binom{2n}{n}}$, and found one congruence and two convergent series on $S_n$ by \ttMathematica. Furthermore, he proposed some related conjectures. In this paper, we first give analytic proofs of his two convergent series and then confirm one of his conjectures by invoking series expansions of $\sin(t\arcsin(x))$ and $\cos(t\arcsin(x)).$
- May 27 2016 math.RA arXiv:1605.08281v1The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.
- Feb 17 2016 math.CO arXiv:1602.04909v1The Catalan-Larcombe-French sequence $\{P_n\}_{n\geq 0}$ arises in a series expansion of the complete elliptic integral of the first kind. It has been proved that the sequence is log-balanced. In the paper, by exploring a criterion due to Chen and Xia for testing 2-log-convexity of a sequence satisfying three-term recurrence relation, we prove that the new sequence $\{P^2_n-P_{n-1}P_{n+1}\}_{n\geq 1}$ are strictly log-convex and hence the Catalan-Larcombe-French sequence is strictly 2-log-convex.
- Feb 16 2016 math.CO arXiv:1602.04359v4Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence $\{P_n\}_{n\geq 0}$ and the Fennessey-Larcombe-French sequence $\{V_n\}_{n\geq 0}$ respectively. In this paper, we prove the log-convexity of $\{V_n^2-V_{n-1}V_{n+1}\}_{n\geq 2}$ and $\{n!V_n\}_{n\geq 1}$, the ratio log-concavity of $\{P_n\}_{n\geq 0}$ and the sequence $\{A_n\}_{n\geq 0}$ of Apéry numbers, and the ratio log-convexity of $\{V_n\}_{n\geq 1}$.
- Reliable and energy-efficient wireless data transmission remains a major challenge in resource-constrained wireless neural recording tasks, where data compression is generally adopted to relax the burdens on the wireless data link. Recently, Compressed Sensing (CS) theory has successfully demonstrated its potential in neural recording application. The main limitation of CS, however, is that the neural signals have no good sparse representation with commonly used dictionaries and learning a reliable dictionary is often data dependent and computationally demanding. In this paper, a novel CS approach for implantable neural recording is proposed. The main contributions are: 1) The co-sparse analysis model is adopted to enforce co-sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis model and enhancing the reconstruction performance. 2) A multi-fractional-order difference matrix is constructed as the analysis dictionary, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational resources. 3) By exploiting the statistical priors of the analysis coefficients, a weighted analysis $\ell_1$-minimization (WALM) algorithm is proposed to reconstruct the neural signals. Experimental results on Leicester neural signal database reveal that the proposed approach outperforms the state-of-the-art CS-based methods. On the challenging high compression ratio task, the proposed approach still achieves high reconstruction performance and spike classification accuracy.
- A universal word for a finite alphabet $A$ and some integer $n\geq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A$ and $n$. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from $A$ may contain an arbitrary number of occurrences of a special `joker' symbol $\Diamond\notin A$, which can be substituted by any symbol from $A$. For example, $u=0\Diamond 011100$ is a linear partial word for the binary alphabet $A=\{0,1\}$ and for $n=3$ (e.g., the first three letters of $u$ yield the subwords $000$ and $010$). We present results on the existence and non-existence of linear and cyclic universal partial words in different situations (depending on the number of $\Diamond$s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.
- We consider the problem of sparse signal recovery from 1-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These sign flips may result in severe performance degradation. In this study, a novel algorithm, termed HISTORY, is proposed. It consists of Hamming support detection and coefficients recovery. The HISTORY algorithm has high recovery accuracy and is robust to strong measurement noise. Numerical results are provided to demonstrate the effectiveness and superiority of the proposed algorithm.
- Dec 04 2015 math.CO arXiv:1512.01008v1Recently, Z. W. Sun put forward a series of conjectures on monotonicity of combinatorial sequences in the form of $\{z_n/z_{n-1}\}_{n=N}^\infty$ and $\{\sqrt[n+1]{z_{n+1}}/\sqrt[n]{z_n}\}_{n=N}^\infty$ for some positive integer $N$, where $\{z_n\}_{n=0}^\infty$ is a sequence of positive integers. Luca and Stănică, Hou et al., Chen et al., Sun and Yang proved some of them. In this paper, we give an affirmative answer to monotonicity of another new kind of number conjectured by Z. W. Sun via interlacing method for log-convexity and log-concavity of a sequence, and we also use the criterion for log-concavity of a sequence in the form of $\{\sqrt[n]{z_n}\}_{n=1}^\infty$ due to Xia.
- Dec 04 2015 math.CO arXiv:1512.01010v1Recently, Z. W. Sun introduced a new kind of numbers $S_n$ and also posed a conjecture on ratio monotonicity of combinatorial sequences related to $S_n$. In this paper, by investigating some arithmetic properties of $S_n$, we give an affirmative answer to his conjecture. Our methods are based on a newly established criterion and interlacing method for log-convexity, and also the criterion for ratio log-concavity of a sequence due to Chen, Guo and Wang.
- Nov 18 2015 math.CO arXiv:1511.05434v2In this paper, we confirm a conjecture of Laborde-Zubieta on the enumeration of corners in tree-like tableaux. Our proof is based on Aval, Boussicault and Nadeau's bijection between tree-like tableaux and permutation tableaux, and Corteel and Nadeau's bijection between permutation tableaux and permutations. This last bijection sends a corner in permutation tableaux to an ascent followed by a descent in permutations, this enables us to enumerate the number of corners in permutation tableaux, and thus to completely solve L.-Z.'s conjecture. Moreover, we give a bijection between corners and runs of size 1 in permutations, which gives an alternative proof of the enumeration of corners. Finally, we introduce an ($a$,$b$)-analogue of this enumeration, and explain the implications on the PASEP.
- Nov 18 2015 math.CO arXiv:1511.05456v4In this paper, we confirm conjectures of Laborde-Zubieta on the enumeration of corners in tree-like tableaux and in symmetric tree-like tableaux. In the process, we also enumerate corners in (type $B$) permutation tableaux and (symmetric) alternative tableaux. The proof is based on Corteel and Nadeau's bijection between permutation tableaux and permutations. It allows us to interpret the number of corners as a statistic over permutations that is easier to count. The type $B$ case uses the bijection of Corteel and Kim between type $B$ permutation tableaux and signed permutations. Moreover, we give a bijection between corners and runs of size 1 in permutations, which gives an alternative proof of the enumeration of corners. Finally, we introduce conjectural polynomial analogues of these enumerations, and explain the implications on the PASEP.
- In this paper, we introduce the concepts of Rota-Baxter operators and differential operators with weights on a multiplicative $n$-ary Hom-algebra. We then focus on Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras and show that they can be derived from Rota-Baxter Hom-Lie algebras, Hom-preLie algebras and Rota-Baxter commutative Hom-associative algebras. We also explore the connections between these Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras.
- Sep 08 2015 math.RT arXiv:1509.01755v3We prove a generalization of Harish-Chandra's character orthogonality relations for discrete series to arbitrary Harish-Chandra modules for real reductive Lie groups. This result is an analogue of a conjecture by Kazhdan for $\mathfrak p$-adic reductive groups proved by Bezrukavnikov, and Schneider and Stuhler.
- Jul 27 2015 math.CO arXiv:1507.06749v2A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $(x,y)\in E$. Halldórsson et al.\ have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary to this result is that any 3-colorable graph is word-representable. Akrobotu et al.\ have shown that a triangulation of a grid graph is word-representable if and only if it is 3-colorable. This result does not hold for triangulations of grid-covered cylinder graphs, namely, there are such word-representable graphs with chromatic number 4. In this paper we show that word-representability of triangulations of grid-covered cylinder graphs with three sectors (resp., more than three sectors) is characterized by avoiding a certain set of six minimal induced subgraphs (resp., wheel graphs $W_5$ and $W_7$).
- Jul 17 2015 math.RT arXiv:1507.04551v1We complete the proof of the Howe duality conjecture in the theory of local theta correspondence by treating the remaining case of quaternionic dual pairs in arbitrary residual characteristic.
- We formulate and prove Chevalley's theorem in the setting of affine Nash groups. As a consequence, we show that the semi-direct product of two almost linear Nash groups is still an almost linear Nash group.
- Jun 10 2015 math.RT arXiv:1506.02766v2In this paper we investigate some methods on calculating the spaces of generalized semi-invariant distributions on p-adic spaces. Using homological methods, we give a criterion of automatic extension of (generalized) semi-invariant distributions. Based on the meromorphic continuations of Igusa zeta integrals, we give another criteria with purely algebraic geometric conditions, on the extension of generalized semi-invariant distributions.
- Mar 30 2015 math.CO arXiv:1503.08002v1A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with equilateral triangles defined by a finite number of triangles, called cells. A subdivision of a triangular grid graph is replacing some of its cells by plane copies of the complete graph $K_4$. Inspired by a recent elegant result of Akrobotu et al., who classified word-representable triangulations of grid graphs related to convex polyominoes, we characterize word-representable subdivisions of triangular grid graphs. A key role in the characterization is played by smart orientations introduced by us in this paper. As a corollary to our main result, we obtain that any subdivision of boundary triangles in the Sierpiński gasket graph is word-representable.
- Feb 12 2015 math.CO arXiv:1502.03294v1Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at $1$, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.
- Jan 05 2015 math.RA arXiv:1501.00229v1We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and Hom-Novikov superalgebras with Rota-Baxter operators, respectively. We show that quadratic Hom-Novikov superalgebras are Hom-associative superalgebras and the sub-adjacent Hom-Lie superalgebras of Hom-Novikov superalgebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of Hom-Novikov superalgebras.
- The development of coherent missing data models to account for nonmonotone missing at random (MAR) data by inverse probability weighting (IPW) remains to date largely unresolved. As a consequence, IPW has essentially been restricted for use only in monotone missing data settings. We propose a class of models for nonmonotone missing data mechanisms that spans the MAR model, while allowing the underlying full data law to remain unrestricted. For parametric specifications within the proposed class, we introduce an unconstrained maximum likelihood estimator for estimating the missing data probabilities which can be easily implemented using existing software. To circumvent potential convergence issues with this procedure, we also introduce a Bayesian constrained approach to estimate the missing data process which is guaranteed to yield inferences that respect all model restrictions. The efficiency of the standard IPW estimator is improved by incorporating information from incomplete cases through an augmented estimating equation which is optimal within a large class of estimating equations. We investigate the finite-sample properties of the proposed estimators in a simulation study and illustrate the new methodology in an application evaluating key correlates of preterm delivery for infants born to HIV infected mothers in Botswana, Africa.
- Nov 22 2013 math.RT arXiv:1311.5321v1Let $k$ be a local field of characteristic zero. Rankin-Selberg's local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of $GL_n(k)\times GL_r(k)$, with certain invariance properties. We show that up to scalar multiplication, these linear functionals are determined by the invariance properties.
- Oct 31 2013 math.RT arXiv:1310.8011v2A Nash group is said to be almost linear if it has a Nash representation with finite kernel. Structures and basic properties of these groups are studied.
- Jul 23 2013 math.RT arXiv:1307.5357v2We prove the nonvanishing hypothesis at infinity for Rankin-Selberg convolutions for $\GL(n)\times \GL(n-1)$.
- Dec 26 2012 math.RT arXiv:1212.6015v1Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show vanishing of quasi-invariant generalized functions, developed in the recent work of the authors (Uniqueness of Ginzburg-Rallis models: the Archimedean case, Trans. Amer. Math. Soc. 363, (2011), 2763-2802). The first two techniques involve geometric notions attached to submanifolds, which we call metrical properness and unipotent $\chi$-incompatibility. The third one is analytic in nature, and it arises from the first occurrence phenomenon in Howe correspondence. We also highlight how these techniques quickly lead to two well-known uniqueness results, on trilinear forms and Whittaker models.
- Sep 17 2012 math.RT arXiv:1209.3075v1We prove uniqueness of Fourier-Jacobi models for general linear groups, unitary groups, symplectic groups and metaplectic groups, over an archimedean local field.
- Apr 16 2012 math.RT arXiv:1204.2969v3We prove Kudla-Rallis conjecture on first occurrences of local theta correspondence, for all type I irreducible dual pairs and all local fields of characteristic zero.
- Let $G$ be a real reductive group, and let $\chi$ be a character of a reductive subgroup $H$ of $G$. We construct $\chi$-invariant linear functionals on certain cohomologically induced representations of $G$, and show that these linear functionals do not vanish on the bottom layers. Applying this construction, we prove two archimedean non-vanishing assumptions, which are crucial in the study of special values of L-functions via modular symbols.
- Nov 14 2011 math.RT arXiv:1111.2635v1Let $G$ be a real quaternionic classical group $\GL_n(\bH)$, $\Sp(p,q)$ or $\oO^*(2n)$. We define an extension $\breve G$ of $G$ with the following property: it contains $G$ as a subgroup of index two, and for every $x\in G$, there is an element $\breve g\in \breve G\setminus G$ such that $\breve g x\breve{g}^{-1}=x^{-1}$. This is similar to Moeglin-Vigneras-Waldspurger's extensions of non-quaternionic classical groups.
- In cognitive radio (CR) networks, the perceived reduction of application layer quality of service (QoS), such as multimedia distortion, by secondary users may impede the success of CR technologies. Most previous work in CR networks ignores application layer QoS. In this paper we take an integrated design approach to jointly optimize multimedia intra refreshing rate, an application layer parameter, together with access strategy, and spectrum sensing for multimedia transmission in a CR system with time varying wireless channels. Primary network usage and channel gain are modeled as a finite state Markov process. With channel sensing and channel state information errors, the system state cannot be directly observed. We formulate the QoS optimization problem as a partially observable Markov decision process (POMDP). A low complexity dynamic programming framework is presented to obtain the optimal policy. Simulation results show the effectiveness of the proposed scheme.
- Mar 03 2011 math.RT arXiv:1103.0356v1We review certain basic geometric and analytic results concerning MVW-extensions of classical groups, following Moeglin-Vigneras-Waldspurger. The related results for Jacobi groups, metaplectic groups, and special orthogonal groups are also included.
- Oct 13 2010 math.FA arXiv:1010.2342v3Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces.
- This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business policies from an available set of control policies with different expected profits and risks, controls the business policy and dividend payout process to maximize the expected present value of the dividends until the time of bankruptcy. However, if the dividend payout barrier is too low to be acceptable, it may result in the company's bankruptcy soon. In order to protect the shareholders' profits, the managements of the company impose a reasonable and normal constraint on their dividend strategy, that is, the bankrupt probability associated with the optimal dividend payout barrier should be smaller than a given risk level within a fixed time horizon. This paper aims at working out the optimal control policy as well as optimal return function for the company under bankrupt probability constraint by stochastic analysis, PDE methods and variational inequality approach. Moreover, we establish a risk-based capital standard to ensure the capital requirement of can cover the total given risk by numerical analysis and give reasonable economic interpretation for the results.
- May 26 2010 math.RT arXiv:1005.4484v2The purpose of this note is to verify that the archimedean multiplicity one theorems shown for orthogonal groups (as well as general linear and unitary groups) in a previous paper of the authors remain valid for special orthogonal groups. The necessary ingredients to establish this variant are due to Waldspurger.
- May 03 2010 math.RT arXiv:1004.5508v2We consider a category of continuous Hilbert space representations and a category of smooth Frechet representations, of a real Jacobi group $G$. By Mackey's theory, they are respectively equivalent to certain categories of representations of a real reductive group $\widetilde L$. Within these categories, we show that the two functors of taking smooth vectors for $G$, and for $\widetilde L$, are consistent with each other. By using Casselman-Wallach's theory of smooth representations of real reductive groups, we define matrix coefficients for distributional vectors of certain representations of $G$. We also formulate Gelfand-Kazhdan criteria for Jacobi groups which could be used to prove the multiplicity one theorem for Fourier-Jacobi models.
- Aug 13 2009 math.RT arXiv:0908.1728v2In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.
- Mar 10 2009 math.RT arXiv:0903.1417v3For every genuine irreducible admissible smooth representation $\pi$ of the metaplectic group $\widetilde{\Sp}(2n)$ over a p-adic field, and every smooth oscillator representation $\omega_\psi$ of $\widetilde{\Sp}(2n)$, we prove that the tensor product $\pi\otimes \omega_\psi$ is multiplicity free as a smooth representation of the symplectic group $\Sp(2n)$. Similar results are proved for general linear groups and unitary groups.
- Mar 10 2009 math.RT arXiv:0903.1413v2Let $G$ be one of the classical Lie groups $\GL_{n+1}(\R)$, $\GL_{n+1}(\C)$, $\oU(p,q+1)$, $\oO(p,q+1)$, $\oO_{n+1}(\C)$, $\SO(p,q+1)$, $\SO_{n+1}(\C)$, and let $G'$ be respectively the subgroup $\GL_{n}(\R)$, $\GL_{n}(\C)$, $\oU(p,q)$, $\oO(p,q)$, $\oO_n(\C)$, $\SO(p,q)$, $\SO_n(\C)$, embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups $\GL_{n}(\R)\ltimes \oH_{2n+1}(\R)$, $\GL_{n}(\C)\ltimes \oH_{2n+1}(\C)$, $\oU(p,q)\ltimes \oH_{2p+2q+1}(\R)$, $\Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R)$, $\Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C)$, with their respective subgroups $\GL_{n}(\R)$, $\GL_{n}(\C)$, $\oU(p,q)$, $\Sp_{2n}(\R)$, $\Sp_{2n}(\C)$.
- Mar 10 2009 math.RT arXiv:0903.1418v2Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient of $\pi$ is isomorphic to a twist of $\pi$ by an automorphism of $G$. We prove a similar result for double covers of $G$ which occur in the study of local theta correspondences.
- Mar 10 2009 math.RT arXiv:0903.1419v1Over a non-archimedean local field of characteristic zero, we prove the multiplicity preservation for orthogonal-symplectic dual pair correspondences and unitary dual pair correspondences.
- Mar 10 2009 math.RT arXiv:0903.1409v6We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion for a real reductive group in very general settings.
- Mar 10 2009 math.RT arXiv:0903.1411v2In this paper, we prove the uniqueness of Ginzburg-Rallis models in the archimedean case. As a key ingredient, we introduce a new descent argument based on two geometric notions attached to submanifolds, which we call metrical properness and unipotent $\chi$-incompatibility.