Joshua M. Lansky
Lifting representations of finite reductive groups I: Semisimple conjugacy classes.
Tue, 06/07/2011 - 15:01 — SomNambulAuthors: Joshua M. Lansky, Jeffrey D. Adler
Subjects: Representation Theory
AbstractSuppose that $\tilde{G}$ is a connected reductive group defined over a field
$k$, $\Gamma$ is a group of $k$-automorphisms of $\tilde{G}$ satisfying a
quasi-semisimplicity condition, and $G$ is the connected part of the group of
fixed points. Then $G$ is reductive. If both $\tilde{G}$ and $G$ are
$k$-quasisplit, then we can consider their duals $\tilde{G}^*$ and $G^*$. We
show the existence and give an explicit formula for a natural map from stable
conjugacy classes in $G^*(k)$ to those in $\tilde{G}^*(k)$.Depth-zero base change for ramified U(2,1).
Mon, 09/28/2009 - 15:24 — SomNambulAuthors: Joshua M. Lansky, Jeffrey D. Adler
Subjects: Representation Theory
AbstractWe give an explicit description of L-packets and quadratic base change for
depth-zero representations of ramified unitary groups in two and three
variables. We show that this base change lifting is compatible with a certain
lifting of families of representations of finite groups. We conjecture that
such a compatibility is valid in much greater generality.Depth-zero base change for ramified U(2,1).
Mon, 09/28/2009 - 15:24 — SomNambulAuthors: Joshua M. Lansky, Jeffrey D. Adler
Subjects: Representation Theory
AbstractWe give an explicit description of L-packets and quadratic base change for
depth-zero representations of ramified unitary groups in two and three
variables. We show that this base change lifting is compatible with a certain
lifting of families of representations of finite groups. We conjecture that
such a compatibility is valid in much greater generality.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.
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