Reducibility of Principal Series Representations of p-Adic Chevalley Groups

Abstract

Introduction. In this paper we study the question of reducibility of principal series representations of p-adic Chevalley groups. Let G be a p-adic Chevalley group, and let B be a Borel subgroup of G. If 'y is an irreducible finite-dimensional unitary representation of B, let lY = Ind y. Then flY is a BIG unitary (principal series) representation of G. It is well known that if w is an element of the restricted Weyl group of G,