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Transactions of the American Mathematical Society

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Square-integrable representations and the Mackey theory

Author: Terje Sund
Journal: Trans. Amer. Math. Soc. 194 (1974), 131-139
MSC: Primary 22D10
MathSciNet review: 0344376
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Abstract: It is the purpose of this paper to clarify the relationship between the square-integrable irreducible representations of a 2nd countable unimodular locally compact group G and a closed normal subgroup N using the Mackey theory relating the dual spaces $ \hat G$ and $ \hat N$.

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Keywords: 2nd countable locally compact group, closed normal type I subgroup, regular embeddedness, continuous unitary representation, dual space, reduced dual, square-integrable irreducible representation, induced representation, action by inner automorphisms, orbits
Article copyright: © Copyright 1974 American Mathematical Society