Cuspidal irreducible complex or l-modular representations of quaternionic forms of p-adic classical groups for odd p

Abstract

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. 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.

arXiv comment1) Proof of Proposition A.1 and Theorem A.2 provided by Prof. Shaun Stevens 2) There is a difference between the quasi-split and the quaternionic case in the choice of standard beta-extension. We needed to invent property (ORD)