MATRIX SPHERICAL ANALYSIS ON NILMANIFOLDS
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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.
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