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On the uniqueness of conical vectors


Author: J. Lepowsky
Journal: Proc. Amer. Math. Soc. 57 (1976), 217-220
MSC: Primary 17B20
DOI: https://doi.org/10.1090/S0002-9939-1976-0409576-8
MathSciNet review: 0409576
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Abstract: Certain conical vectors in induced modules for semisimple symmetric Lie algebras have been determined in a previous paper. Here the uniqueness aspects of those results are proved in a simpler way, and a refinement of one of the earlier results is given.


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

  • [1] J. Dixmier, Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. MR 0498737 (58:16803a)
  • [2] J. Lepowsky, On the Harish-Chandra homomorphism, Trans. Amer. Math. Soc. 208 (1975), 193-218. MR 0376792 (51:12967)
  • [3] -, Conical vectors in induced modules, Trans. Amer. Math. Soc. 208 (1975), 219-272. MR 0376786 (51:12961)
  • [4] -, Uniqueness of embeddings of certain induced modules, Proc. Amer. Math. Soc. 56 (1976), 55-58. MR 0399195 (53:3046)
  • [5] G. Warner, Harmonic analysis on semi-simple Lie groups. I, Die Grundlehren der math. Wissenschaften, Band 188, Springer-Verlag, New York, 1972. MR 0498999 (58:16979)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409576-8
Keywords: Conical vectors, algebraically induced modules, semisimple symmetric Lie algebras
Article copyright: © Copyright 1976 American Mathematical Society

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