 |
|
Reducibility for $SU_n$ and Generic Elliptic Representations |
Canad. J. Math. 58(2006), 344-361
Published:2006-04-01
Printed: Apr 2006
Printed: Apr 2006
- David Goldberg
Abstract
We study reducibility of representations
parabolically induced from discrete series
representations of $SU_n(F)$ for $F$ a $p$-adic field of
characteristic zero. We use the approach of studying the relation
between $R$-groups when a reductive subgroup of a quasi-split group
and the full group have the same derived group. We use restriction to
show the quotient of $R$-groups is in natural bijection with a group
of characters. Applying this to $SU_n(F)\subset U_n(F)$ we show the
$R$ group for $SU_n$ is the semidirect product of an $R$-group for
$U_n(F)$ and this group of characters. We derive results on
non-abelian $R$-groups and generic elliptic representations as well.
| MSC Classifications: |
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 22E35 - Analysis on $p$-adic Lie groups |