Cyclic vectors and irreducibility for principal series representations. II
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- by Nolan R. Wallach PDF
- Trans. Amer. Math. Soc. 164 (1972), 389-396 Request permission
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
- Harish-Chandra, Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc. 76 (1954), 234–253. MR 62747, DOI 10.1090/S0002-9947-1954-0062747-5
- Harish-Chandra, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc. 76 (1954), 485–528. MR 63376, DOI 10.1090/S0002-9947-1954-0063376-X
- Sigurđur Helgason, Lie groups and symmetric spaces, Battelle Rencontres. 1967 Lectures in Mathematics and Physics, Benjamin, New York, 1968, pp. 1–71. MR 0236325
- Bertram Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627–642. MR 245725, DOI 10.1090/S0002-9904-1969-12235-4 —, (to appear).
- Nolan R. Wallach, Cyclic vectors and irreducibility for principal series representations, Trans. Amer. Math. Soc. 158 (1971), 107–113. MR 281844, DOI 10.1090/S0002-9947-1971-0281844-2
- D. P. Želobenko, The analysis of irreducibility in the class of elementary rupresentations of a semisimple complex Lie group, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 108–133 (Russian). MR 0227321
Additional Information
- © Copyright 1972 American Mathematical Society
- 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