On induced representations of discrete groups

Binder, Michael W.

doi:10.1090/S0002-9939-1993-1123649-6

On induced representations of discrete groups
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by Michael W. Binder PDF

Proc. Amer. Math. Soc. 118 (1993), 301-309 Request permission

Abstract:

The paper deals with induced representations $\operatorname {ind} _H^G\sigma$ of a locally compact group $G$ where $H$ is an open subgroup. Using "elementary intertwining operators", we first describe the commutant $\operatorname {ind} _H^G\sigma (G)’$ (also in the case of realizing the induced representations with positive definite measures). Then criteria for irreducibility and pairwise disjointness of induced representations are given. Finally, special attention is devoted to abelian subgroups $H$.

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