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Transactions of the American Mathematical Society

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Cyclic vectors and irreducibility for principal series representations. II


Author: Nolan R. Wallach
Journal: Trans. Amer. Math. Soc. 164 (1972), 389-396
MSC: Primary 22E45
DOI: https://doi.org/10.1090/S0002-9947-1972-0320233-X
MathSciNet review: 0320233
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Abstract: This paper is a continuation of the author's paper Cyclic vectors and irreducibility for principal series representations. In this paper the nonunitary principal series is studied. Using a theorem of Kostant, a sufficient condition is found for irreducibility of nonunitary principal series representations.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0320233-X
Keywords: Representation, Hilbert space, character, universal enveloping algebra, irreducible, admissible, Haar measure, trace class, module, root, Weyl group, Peter-Weyl Theorem
Article copyright: © Copyright 1972 American Mathematical Society