关键词: pseudo-Riemannian symmetric space, spherical distributions, Poisson kernels, Casimir operators, Plancherel formula

Abstract: In this paper we obtain the Plancherel formula for the spaces of L²-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL(n + 1, R) and H=S(GL(1, R)×GL(n, R)). The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χ_λ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.

Key words: pseudo-Riemannian symmetric space, spherical distributions, Poisson kernels, Casimir operators, Plancherel formula