Weak containment and weak Frobenius reciprocity
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- by Elliot C. Gootman PDF
- Proc. Amer. Math. Soc. 54 (1976), 417-422 Request permission
Abstract:
We study weak containment relations between unitary representations of a group $G$ and a closed normal subgroup $K$ by exploiting a property of $G$-ergodic quasi-invariant measures on the primitive ideal space of $K$. By this means, we prove that every irreducible representation of $G$ is weakly contained in a representation induced from an irreducible representation of $K$ if the quotient group $G/K$ is amenable; and that the pair $(G,K)$ satisfies a weak Frobenius reciprocity property if and only if $G/K$ is amenable and $G$ acts minimally on the primitive ideal space of $K$. If $G/K$ is compact, $G$ acts minimally if and only if the primitive ideal space of $K$ is ${T_1}$.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 417-422
- MSC: Primary 22D10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0435286-7
- MathSciNet review: 0435286