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Weak Containment and Weak Frobenius Reciprocity
Elliot C. Gootman
Proceedings of the American Mathematical Society
Vol. 54, No. 1 (Jan., 1976), pp. 417-422
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040832
Page Count: 6
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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 T1.
Proceedings of the American Mathematical Society © 1976 American Mathematical Society