C. Ryan Vinroot
Klyachko models of p-adic special linear groups.
Wed, 09/02/2009 - 12:02 — SomNambulAuthors: C. Ryan Vinroot, Joshua M. Lansky
Subjects: Representation Theory
AbstractWe study Klyachko models of ${\rm SL}(n, F)$, where $F$ is a nonarchimedean
local field. In particular, using results of Klyachko models for ${\rm GL}(n,
F)$ due to Heumos, Rallis, Offen and Sayag, we give statements of existence,
uniqueness, and disjointness of Klyachko models for admissible representations
of ${\rm SL}(n, F)$, where the uniqueness and disjointness are up to specified
conjugacy of the inducing character, and the existence is for unitarizable
representations in the case $F$ has characteristic 0.Klyachko models of p-adic special linear groups.
Wed, 09/02/2009 - 12:02 — SomNambulAuthors: C. Ryan Vinroot, Joshua M. Lansky
Subjects: Representation Theory
AbstractWe study Klyachko models of ${\rm SL}(n, F)$, where $F$ is a nonarchimedean
local field. In particular, using results of Klyachko models for ${\rm GL}(n,
F)$ due to Heumos, Rallis, Offen and Sayag, we give statements of existence,
uniqueness, and disjointness of Klyachko models for admissible representations
of ${\rm SL}(n, F)$, where the uniqueness and disjointness are up to specified
conjugacy of the inducing character, and the existence is for unitarizable
representations in the case $F$ has characteristic 0.Character degree sums and real representations of finite classical groups of odd characteristic.
Tue, 08/18/2009 - 11:53 — SomNambulAuthors: C. Ryan Vinroot
Subjects: Representation Theory
AbstractLet $\mathbb{F}_q$ be a finite field with $q$ elements, where $q$ is the
power of an odd prime, and let $\mathrm{GSp}(2n, \mathbb{F}_q)$ and
$\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ denote the symplectic and orthogonal
groups of similitudes over $\mathbb{F}_q$, respectively. We prove that every
real-valued irreducible character of $\mathrm{GSp}(2n, \mathbb{F}_q)$ or
$\mathrm{GO}^{\pm}(2n, \mathbb{F}_q)$ is the character of a real
representation, and we find the sum of the dimensions of the real
representations of each of these groups.
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