The explicit Plancherel formula on the line budle of $\mathrm{SL}(n+1,\mathbb{R})/\mathrm{S}(\mathrm{GL}(1,\mathbb{R})\times \mathrm{GL}(n,\mathbb{R}))$

Li Zhu, Liangyun Chen

The purpose of this paper is to study the Plancherel formula for the spaces of $L^2$-sections of the line bundles over the pseudo-Riemannian space $G/H$, where $G={\rm SL}(n+1, {\m…