The Plancherel Formula of $L^2(N_0\setminus G;\psi )$

We study the right regular representation on the space $L^2(N_0\setminus G;\psi)$where$G$isaquasi-split$p$-adicgroupand$\psi$ a non-degenerate unitary character of the unipotent subgroup $N_0$ 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 $L^2(N_0\setminus G;\psi )$ consists precisely of $\psi$ generic discrete series representations and derive the Plancherel formula for $L^2(N_0\setminus G;\psi )$.