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Constructing irreducible representations of discrete groups

Burger, Marc ; De La Harpe, Pierre

In: Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 1997, vol. 107, no. 3, p. 223-235

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    Title
    • Constructing irreducible representations of discrete groups
    Author
    • Burger, Marc. Institut de Mathématiques, Université de Lausanne, Dorigny, CH-1015, Lausanne, Suisse
    • De La Harpe, Pierre. Section de Mathématiques, Université de Genève, C.P. 240, CH-1211, Genève 24, Suisse
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 1997, vol. 107, no. 3, p. 223-235. Springer Netherlands
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:314603
    Summary
    The decomposition of unitary representations of a discrete group obtained by induction from a subgroup involves commensurators. In particular Mackey has shown that quasi-regular representations are irreducible if and only if the corresponding subgroups are self-commensurizing. The purpose of this work is to describe general constructions of pairs of groups Γ0 with Γ its own commensurator in Γ. These constructions are then applied to groups of isometries of hyperbolic spaces and to lattices in algebraic groups