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

Abstract

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 $G=\mathrm{SL}(n+1,\mathbb{R})$ and $H=\mathrm{S}(\mathrm{GL}(1,\mathbb{R})\times \mathrm{GL}(n,\mathbb{R}))$. The formula is given in an explicit form by means of spherical distributions associated with the character ${\chi }_{{}_{\lambda }}$ of the subgroup $H$.

Several theorems in this paper are wrong

References in corpus (2)

• Classification of discretely decomposable A_q(λ) with respect to reductive symmetric pairs
• A Plancherel formula for L^2(G/H) for almost symmetric subgroups