Subrepresentations of direct integrals and finite volume homogeneous spaces

Author:
Elliot C. Gootman

Journal:
Proc. Amer. Math. Soc. **88** (1983), 565-568

MSC:
Primary 22D30; Secondary 46A35

DOI:
https://doi.org/10.1090/S0002-9939-1983-0699435-1

MathSciNet review:
699435

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Abstract: We prove a result on representations of separable -algebras which has application to, and was in fact motivated by, a problem concerning relations between unitary representations of a second countable locally compact group and those of a closed subgroup , when is of finite volume. The result is that if an irreducible representation is contained in , then for all in a set of positive measure. With and as above, it follows that for each there exists with , the induced representation. Frobenius reciprocity type results are derived as further consequences.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0699435-1

Article copyright:
© Copyright 1983
American Mathematical Society