Discrete Series for p-adic SO(2n) and Restrictions of Representations of O(2n)

Abstract

Abstract In this paper we give a classification of discrete series for SO(2n, F), F p-adic, similar to that of Mœglin–Tadić for the other classical groups. This is obtained by taking the Mœglin–Tadić classification for O(2n, F) and studying how the representations restrict to SO(2n, F). We then extend this to an analysis of how admissible representations of O(2n, F) restrict.