Reducibility for $S{U}_n$ and generic elliptic representations

Abstract

We examine the reducibility of induced from discrete series representations of $S{U}_n$ over a $p$--adic field of characteristic zero. Some results are given for groups sharing derived group. We give a relationship between the $R$-groups for $U)n$ and $S{U}_n.$ Nonabelian $R$-groups are discussed. Elliptic representations are examined and in the generic case we give an explicit description f those $L$--packets containing non-discrete elliptic tempered representations. We exhibit $L$--packets containing both elliptic and non-elliptic components.