Expand all Collapse all | Results 1 - 7 of 7 |
1. CMB Online first
Quantum unique ergodicity on locally symmetric spaces: the degenerate lift iven 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)
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 induction Category:22E50 |
3. CMB 2007 (vol 50 pp. 440)
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)
On the Structure of the Full Lift for the Howe Correspondence of $(Sp(n), O(V))$ for Rank-One Reducibilities |
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)
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)
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)
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 |