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

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

Categories: math.DG math.RA