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Irreducibility of certain degenerate principal series representations of $ {\rm Sp}(n,\,{\bf R})$


Author: Thomas A. Farmer
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
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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 [Enhancements On Off] (What's this?)

  • [1] G. Carrier, M. Krook and C. Pearson, Functions of a complex variable, McGraw-Hill, New York, 1966. MR 0222256 (36:5308)
  • [2] T. Farmer, On the reduction of certain degenerate principal series representations of $ {\text{Sp}}(n,{\mathbf{C}})$, Pacific J. Math. 84 (1979), 291-303. MR 568652 (83m:22023)
  • [3] K. I. Gross, The dual of a parabolic subgroup and a degenerate principal series of $ {\text{Sp}}(n,{\mathbf{C}})$, Amer. J. Math. 93 (1971), 398-428. MR 0304558 (46:3693)
  • [4] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, 2nd ed., Clarendon Press, Oxford, 1948.
  • [5] J. A. Wolf, Unitary representations of maximal parabolic subgroups of the classical groups, Mem. Amer. Math. Soc., no. 180, 1976. MR 0444847 (56:3194)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624943-7
Article copyright: © Copyright 1981 American Mathematical Society

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