Let $G$ be a connected real semisimple or reductive Lie group. Let $TA$ be a Cartan subgroup, where $T$ is compact and $A$ is split. Let $MA$ be the centralizer of $A$ in $G$, and let $N$ be the nilpotent subgroup corresponding to some positive system of $A$. Then $P = MAN$ is a cuspidal parabolic subgroup of $G$. Using the left $G$-action on $G/N$, equip $G/N$ with a $G$-invariant measure. Then $L^2(G/N)$ is a unitary representation of $G \times M$ (left $G$ and right $M$). What is the Plancherel formula for the unitary $G$-representation on $L^2(G/N)$? In Wallach's book "Real Reductive Groups II" Section 15, this is given for minimal parabolic $P$. I hope to get the answer for more general $P$.
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