The plancherel Formula of L^2(N_0 GIpsi) where G is a p-adic group

Abstract

We study the right regular representation on homogeneous space N\G where G is a quasi-split p-adic group and and N transforms according to a nondegenerate unitary character of the unipotent subgroup N of a minimal parabolic subgroup of G. We obtain the direct integral decomposition of this space into its constituent representations. In particular, we deduce that the discrete spectrum of this representation consists precisely of the generic discrete series representations and derive its Plancherel formula.