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Reducibility for $SU_n$ and Generic Elliptic Representations

  Published:2006-04-01
 Printed: Apr 2006
  • David Goldberg
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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, 22E35 show english descriptions Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Analysis on $p$-adic Lie groups
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
22E35 - Analysis on $p$-adic Lie groups
 

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