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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/107/03/0223-0235

    • Keywords

       

      Commensurator subgroups; unitary representations; quasi-regular representations; Gromov hyperbolic groups; arthmetic lattices

    • Abstract

       

      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.

    • Author Affiliations

       

      Marc Burger1 Pierre De La Harpe2

      1. Institut de Mathématiques, Université de Lausanne, Dorigny, Lausanne - CH-1015, Suisse
      2. Section de Mathématiques, Université de Genève, C.P. 240, Genève 24 - CH-1211, Suisse
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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