Matrix Spherical Analysis on Nilmanifolds

DÍAZ MARTÍN, ROCÍO; SAAL, LINDA

TRANSFORMATION GROUPS

BIRKHAUSER BOSTON INC

Año: 2019 vol. 24 p. 887 - 911

1083-4362

Given a nilpotent Lie group N, a compact subgroup K of automorphisms of N and an irreducible unitary representation (τ,Wτ) of K, we study conditions on τ for the commutativity of the algebra of End(Wτ)-valued integrable functions on N, with an additional property that generalizes the notion of K-invariance. A necessary condition, proved by F. Ricci and A. Samanta, is that (K⋉N,K) must be a Gelfand pair. In this article we determine all the commutative algebras from a particular class of Gelfand pairs constructed by J. Lauret.