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Constructing irreducible representations of discrete groups

Burger, Marc
Published in Proceedings of the Indian Academy of Sciences. Mathematical Sciences. 1997, vol. 107, no. 3, p. 223-235
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 F 0 < F with F 0 its own commensurator in F. These constructions are then applied to groups of isometries of hyperbolic spaces and to lattices in algebraic groups.
Keywords Commensurator subgroupsUnitary representationsQuasi-regular representationsGromov hyperbolic groupsArithmetic lattices
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Deposited on : 2010-12-06

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