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Free group representations from vector-valued multiplicative functions, I

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Abstract

Let Γ denote a noncommutative free group and let Ω stand for its boundary. We construct a large class of unitary representations of Γ. This class contains many previously studied representations, and is closed under several natural operations. Each of the constructed representations is in fact a representation of Γ ⋉λ C(Ω). We prove here that each of them is irreducible as a representation of Γ ⋉λ C(Ω). Actually, as will be shown in further work, each of them is irreducible as a representation of Γ, or is the direct sum of exactly two irreducible, inequivalent Γ-representations.

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Authors and Affiliations

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

    M. Gabriella Kuiin

  2. Struttura di Matematica e Fisica, Università di Sassari, Via Vienna 2, 07100, Sassari, Italy

    Tim Steger

Authors
  1. M. Gabriella Kuiin
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  2. Tim Steger
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Correspondence to M. Gabriella Kuiin.

Additional information

This research was supported by the Italian CNR.

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Kuiin, M.G., Steger, T. Free group representations from vector-valued multiplicative functions, I. Isr. J. Math. 144, 317–341 (2004). https://doi.org/10.1007/BF02916716

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  • DOI: https://doi.org/10.1007/BF02916716

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