On the cuspidal support of discrete series for $p$-adic quasisplit $Sp(N)$ and $SO(N)$

Abstract

Zelevinsky's classification theory of discrete series of $p$-adic general linear groups has been well known. M{\oe}glin and Tadic gave the same kind of theory for $p$-adic classical groups, which is more complicated due to the occurrence of nontrivial structure of L-packets. Nonetheless, their work is independent of the endoscopic classification theory of Arthur (also Mok in the unitary case), which concerns the structure of L-packets in these cases. So our goal in this paper is to make more explicit the connection between these two very different types of theories. To do so, we reprove the results of M{\oe}glin and Tadic in the case of quasisplit symplectic groups and orthogonal groups by using Arthur's theory.