Topological irreducibility of nonunitary representations of group extensions
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- by Floyd L. Williams PDF
- Trans. Amer. Math. Soc. 233 (1977), 69-84 Request permission
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.References
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- George W. Mackey, Induced representations of groups and quantum mechanics, W. A. Benjamin, Inc., New York-Amsterdam; Editore Boringhieri, Turin, 1968. MR 0507212
- Calvin C. Moore and Joseph A. Wolf, Totally real representations and real function spaces, Pacific J. Math. 38 (1971), 537–542. MR 310130, DOI 10.2140/pjm.1971.38.537
- Ernest Thieleker, On the irreducibility of nonunitary induced representations of certain semidirect products, Trans. Amer. Math. Soc. 164 (1972), 353–369. MR 293017, DOI 10.1090/S0002-9947-1972-0293017-9
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 233 (1977), 69-84
- MSC: Primary 22E45
- DOI: https://doi.org/10.1090/S0002-9947-1977-0463364-0
- MathSciNet review: 0463364