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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Topological irreducibility of nonunitary representations of group extensions

Author: Floyd L. Williams
Journal: Trans. Amer. Math. Soc. 233 (1977), 69-84
MSC: Primary 22E45
MathSciNet review: 0463364
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Abstract: A functional-analytic approach to the study of the topological irreducibility of certain nonunitary induced representations is set forth. The methods contrast, and in some sense, encompass those first initiated by E. Thieleker in [4], and are amenable to complete irreducibility questions as well. Several sufficient conditions for topological irreducibility are established. A sufficient condition for reducibility is also presented—the latter serving to explain an interesting counterexample due to J. M. G. Fell.

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Keywords: Lie group, Lie algebra, nonunitary representations, induced representations, topological irreducibility, Hilbert space
Article copyright: © Copyright 1977 American Mathematical Society