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Cuspidal irreducible representations of quaternionic forms of p-adic classical groups for odd p

Research paper by Daniel Skodlerack

Indexed on: 10 May '20Published on: 05 Jul '19Published in: arXiv - Mathematics - Representation Theory



Abstract

Given a quaternionic form G of a p-adic classical group ($p$ odd) we classify all cuspidal irreducible complex representations of G. It is a straight forward generalization of the classification in the p-adic classical group case. We prove two theorems: At first: Every irreducible cuspidal representation of G is induced from a cuspidal type, i.e. from a certain irreducible representation of a compact open subgroup of G, constructed from a beta-extension and a cuspidal representation of a finite group. Secondly we show that two intertwining cuspidal types of G are up to equivalence conjugate under some element of G.