Journal of Lie Theory Volume 7 (1996) 1–28 C ◯1996 Heldermann Verlag

Spherical distributions on harmonic extensions of pseudo-H-type groups

Paolo Ciatti

Communicated by G. Mauceri

Abstract. In the articles “Ciatti, P., Scalar products on Clifford modules and pseudo- H -type Lie algebras, Ann. Mat. Pura Appl., to appear” and “Ciatti, P., Solvable extensions of pseudo- H -type algebras, Boll. Un. Mat. It., to appear,” a class of solvable pseudo-Riemannian harmonic manifolds was constructed. Now spherical distributions on such manifolds are investigated. A notion of radiality for distributions is introduced with the aid of a technique due to J. Faraut (Faraut, J., Distributions sphérique sur les espaces hyperboliques, J. Math. Pures Appl., (1979), 369–444). The spherical distributions are the radial eigendistributions of the Laplace-Beltrami operator. They span a space which, depending on the signature of the metric, may have dimension one or two.

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino ciatti@polito.it

Received February 2, 1996 and in final form November 18, 1996

ISSN 0949–5932 / $2.50 ^{_{C} ◯} Heldermann Verlag