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Search: MSC category 22E50 ( Representations of Lie and linear algebraic groups over local fields [See also 20G05] )

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1. CMB 2015 (vol 58 pp. 632)

Silberman, Lior
 Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift Given a measure $\bar\mu_\infty$ on a locally symmetric space $Y=\Gamma\backslash G/K$, obtained as a weak-{*} limit of probability measures associated to eigenfunctions of the ring of invariant differential operators, we construct a measure $\bar\mu_\infty$ on the homogeneous space $X=\Gamma\backslash G$ which lifts $\bar\mu_\infty$ and which is invariant by a connected subgroup $A_{1}\subset A$ of positive dimension, where $G=NAK$ is an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, then $\bar\mu_\infty$ is also the limit of measures associated to Hecke eigenfunctions on $X$. This generalizes results of the author with A. Venkatesh in the case where the spectral parameters stay away from the walls of the Weyl chamber. Keywords:quantum unique ergodicity, microlocal lift, spherical dualCategories:22E50, 43A85

2. CMB 2012 (vol 56 pp. 647)

Valverde, Cesar
 On Induced Representations Distinguished by Orthogonal Groups Let $F$ be a local non-archimedean field of characteristic zero. We prove that a representation of $GL(n,F)$ obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic. Keywords:distinguished representation, parabolic inductionCategory:22E50

3. CMB 2007 (vol 50 pp. 440)

Raghuram, A.
 A KÃ¼nneth Theorem for $p$-Adic Groups Let $G_1$ and $G_2$ be $p$-adic groups. We describe a decomposition of ${\rm Ext}$-groups in the category of smooth representations of $G_1 \times G_2$ in terms of ${\rm Ext}$-groups for $G_1$ and $G_2$. We comment on ${\rm Ext}^1_G(\pi,\pi)$ for a supercuspidal representation $\pi$ of a $p$-adic group $G$. We also consider an example of identifying the class, in a suitable ${\rm Ext}^1$, of a Jacquet module of certain representations of $p$-adic ${\rm GL}_{2n}$. Categories:22E50, 18G15, 55U25

4. CMB 2006 (vol 49 pp. 578)

Muić, Goran
 On the Structure of the Full Lift for the Howe Correspondence of $(Sp(n), O(V))$ for Rank-One Reducibilities In this paper we determine the structure of the full lift for the Howe correspondence of $(Sp(n),O(V))$ for rank-one reducibilities. Categories:22E35, 22E50, 11F70

5. CMB 2002 (vol 45 pp. 220)

Hakim, Jeffrey; Murnaghan, Fiona
 Globalization of Distinguished Supercuspidal Representations of $\GL(n)$ An irreducible supercuspidal representation $\pi$ of $G= \GL(n,F)$, where $F$ is a nonarchimedean local field of characteristic zero, is said to be distinguished'' by a subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if $\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue of this notion for and irreducible, automorphic, cuspidal representation associated to $\GL(n)$. Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided. Categories:22E50, 22E35, 11F70

6. CMB 2000 (vol 43 pp. 380)

Shahidi, Freydoon
 Twists of a General Class of $L$-Functions by Highly Ramified Characters It is shown that given a local $L$-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial $L$-function. Categories:11F70, 22E35, 22E50

7. CMB 1999 (vol 42 pp. 393)

Savin, Gordan
 A Class of Supercuspidal Representations of $G_2(k)$ Let $H$ be an exceptional, adjoint group of type $E_6$ and split rank 2, over a $p$-adic field $k$. In this article we discuss the restriction of the minimal representation of $H$ to a dual pair $\PD^{\times}\times G_2(k)$, where $D$ is a division algebra of dimension 9 over $k$. In particular, we discover an interesting class of supercuspidal representations of $G_2(k)$. Categories:22E35, 22E50, 11F70
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