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. Mœglin 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 Mœglin and Tadic in the case of quasisplit symplectic groups and orthogonal groups by using Arthur's theory.

Cited by in corpus (8)

• The explicit Zelevinsky-Aubert duality
• On Mœglin's parametrization of Arthur packets for p-adic quasisplit $Sp(N)$ and $SO(N)$
• Simple supercuspidal L-packets of quasi-split classical groups
• Endoscopic lifting of simple supercuspidal representations of SO(2n+1) to GL(2n)
• An averaging formula for the cohomology of PEL-type Rapoport--Zink spaces
• On an algorithm to compute derivatives
• Theta Correspondence and Arthur packets
• Jacquet modules and local Langlands correspondence