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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Irreducibility of certain degenerate principal series representations of $\textrm {Sp}(n, \textbf {R})$
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by Thomas A. Farmer PDF
Proc. Amer. Math. Soc. 83 (1981), 411-420 Request permission

Abstract:

An irreducibility theorem is proved for degenerate principal series representations of ${\text {Sp}}(n,{\mathbf {R}})$ induced from unitary characters of a certain maximal parabolic subgroup.
References
  • George F. Carrier, Max Krook, and Carl E. Pearson, Functions of a complex variable: Theory and technique, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222256
  • Thomas A. Farmer, On the reduction of certain degenerate principal series representations of $\textrm {SP}(n,\,\textbf {C})$, Pacific J. Math. 84 (1979), no. 2, 291–303. MR 568652
  • Kenneth I. Gross, The dual of a parabolic subgroup and a degenerate principal series of $\textrm {Sp}(n,\,\textbf {C})$, Amer. J. Math. 93 (1971), 398–428. MR 304558, DOI 10.2307/2373384
  • E. C. Titchmarsh, Introduction to the theory of Fourier integrals, 2nd ed., Clarendon Press, Oxford, 1948.
  • Joseph A. Wolf, Unitary representations of maximal parabolic subgroups of the classical groups, Mem. Amer. Math. Soc. 8 (1976), no. 180, iii+193. MR 444847, DOI 10.1090/memo/0180
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 411-420
  • MSC: Primary 22E46; Secondary 22D30
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0624943-7
  • MathSciNet review: 624943