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

Published:2011-01-17
Printed: Apr 2011
• Chris Jantzen,
Department of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.
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## 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.
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]