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 $H$.