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Free group representations from vector-valued multiplicative functions, II

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Abstract

Let \(\Gamma \) be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of \(\Gamma \) and proved them irreducible as representation of \(\Gamma \ltimes _\lambda C(\Omega )\). In this paper we analyze multiplicative representations as representations of \(\Gamma \) and we prove a criterium for irreducibility based on the growth of their matrix coefficients.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano “Bicocca”, Edificio U5 Via Cozzi 53, 20125, Milan, Italy

    M. Gabriella Kuhn

  2. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell’ateneo lucano 10, 85100, Potenza, Italy

    Sandra Saliani

  3. Matematica, Università degli Studi di Sassari, Via Piandanna 4, 07100, Sassari, Italy

    Tim Steger

Authors
  1. M. Gabriella Kuhn
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  2. Sandra Saliani
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  3. Tim Steger
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Correspondence to M. Gabriella Kuhn.

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Kuhn, M.G., Saliani, S. & Steger, T. Free group representations from vector-valued multiplicative functions, II. Math. Z. 284, 1137–1162 (2016). https://doi.org/10.1007/s00209-016-1692-z

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  • DOI: https://doi.org/10.1007/s00209-016-1692-z

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