A variant of the Frobenius reciprocity for restricted representations on nilpotent Lie groups

摘要

Let G be a nilpotent connected and simply connected Lie group, K an analytic subgroup of G and π a unitary and irreducible representation of G. We study in this paper a variant of the Frobenius reciprocity for the restricted representation π|K of π on K. It consists in proving that generically, the multiplicity of any isotopic component involved in the central canonical disintegration of cπKoincides with t|he dimension of a certain space generalized tempered distributions which are semi-invariant under the action of a subgroup of K. This problem was considered and partially solved in our previous work 1.