Degenerate principal series in the general case

Abstract

Let $G_n$ denote either the group $SO(2n+1,F)$, $Sp(2n,F)$, or $GSpin(2n+1,F)$ over a non-archimedean local field of characteristic different than two. We determine all composition factors of degenerate principal series of $G_n$, using methods based on the Aubert involution and known results on irreducible subquotiens of the generalized principal series of particular type.