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 dual Categories:22E50, 43A85 

2. CMB 2012 (vol 56 pp. 647)
 Valverde, Cesar

On Induced Representations Distinguished by Orthogonal Groups
Let $F$ be a local nonarchimedean 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 induction Category: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)
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)
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 
