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

Part of the Lecture Notes in Mathematics book series (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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© 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

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