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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.


References [Enhancements On Off] (What's this?)

  • [1] Harish-Chandra, Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc. 76 (1954), 234-253. MR 16, 11. MR 0062747 (16:11e)
  • [2] -, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc. 76 (1954), 485-528. MR 16, 111. MR 0063376 (16:111f)
  • [3] S. Helgason, Lie groups and symmetric spaces, Battelle Rencontres. 1967 Lectures in Math. and Phys., Benjamin, New York, 1968, pp. 1-71. MR 38 #4622. MR 0236325 (38:4622)
  • [4] B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627-642. MR 39 #7031. MR 0245725 (39:7031)
  • [5] -, (to appear).
  • [6] N. Wallach, Cyclic vectors and irreducibility for principal series representations, Trans. Amer. Math. Soc. 158 (1971), 107-113. MR 0281844 (43:7558)
  • [7] D. Želobenko, The analysis of irreducibility in the class of elementary representations of a semisimple complex Lie group, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 108-133 = Math. USSR Izv. 2 (1968), 105-128. MR 37 #2906. MR 0227321 (37:2906)

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Additional Information

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

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