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Non Commutative Harmonic Analysis and Lie Groups pp 91–101Cite as

K-finite joint eigenfunctions of U(g)K on a non-riemannian semisimple symmetric space G/H

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 880))

Abstract

Using a duality introduced in a previous paper we indicate the construction by means of simple integral formulas of a large class of joint eigenfunctions of U(g)K on a semisimple symmetric space. In the special case of a semisimple Lie group considered as a symmetric space, we obtain in this way the spherical trace function corresponding to a minimal K-type (in the sense of Vogan) for many of the irreducible Harish-Chandra modules (maybe all). Detailed proofs are to appear elsewhere.

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References

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Authors and Affiliations

  1. Dept. of Math. and Stat., Royal Veterinary- and Agricultural University, Thorvaldsensvej 40, DK-1871, Copenhagen V, Denmark

    Mogens Flensted-Jensen

Authors
  1. Mogens Flensted-Jensen
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Jacques Carmona Michèle Vergne

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© 1981 Springer-Verlag

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Flensted-Jensen, M. (1981). K-finite joint eigenfunctions of U(g)K on a non-riemannian semisimple symmetric space G/H. In: Carmona, J., Vergne, M. (eds) Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090406

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  • DOI: https://doi.org/10.1007/BFb0090406

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10872-6

  • Online ISBN: 978-3-540-38783-1

  • eBook Packages: Springer Book Archive

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