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MATRIX SPHERICAL ANALYSIS ON NILMANIFOLDS

  • R. DÍAZ MARTÍNEmail author
  • L. SAAL
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Abstract

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 (KN, 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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Authors and Affiliations

  1. 1.CIEM–FaMAF (CONICET)Universidad Nacional de CórdobaCórdobaArgentina
  2. 2.FaMAFUniversidad Nacional de CórdobaCórdobaArgentina

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