  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 $H$.
