Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula

@inproceedings{Ban2006InvariantDO,
  title={Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula},
  author={Erik P. van den Ban},
  year={2006}
}
  • Erik P. van den Ban
  • Published 2006
Let G be a connected real semisimple Lie group with finite centre, and let z be an involutive automorphism of G. Put G'={x~G: z(x)=x}, and let H be a closed subgroup of G with (G'),cHcG'; here (G'), denotes the identity component of GL In this paper we investigate some properties of the algebra D(X) of invariant differential operators on the semisimple symmetric space X=G/H. Our main results are that the action of D(X) diagonalizes over the discrete part of L2(X) (Theorem 1.5), and that the… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 23 references

A description of discrete series for semisimple symmetric spaces, Adv

  • T. OSHIMA, T. MATSUKt
  • Stud. Pure Math
  • 1984
1 Excerpt

Differential equations and semisimple Lie groups. Unpublished manuscript (1960)

  • A HARtSH-CMANDP
  • Collected Papers Vol. HI,
  • 1984
1 Excerpt

Harmonic Analysis on Semi-Simple Lie Groups I, Springer-Verlag, Berlin--New York 1972

  • G. WARNER
  • Received Dec
  • 1984

On generalized Gelfand pairs, Proe

  • G. VAN DISK
  • Japan Acad., Set. A
  • 1984
1 Excerpt

Asymptotic behavior of matrix coefficients of admissible representations

  • W. CASSELMAN, D. MILItia
  • Duke Math. J
  • 1982

Characters of the discrete series for pseudo-Riemannian symmetric spaces. In: Representation Theory of Reductive Groups

  • T. KENGMANA
  • Proc. of the univ. of Utah Conf
  • 1982
1 Excerpt

A description of discrete series for semisimple symmetric spaces

  • T. MATSUKt
  • Adv . Stud . Pure Math
  • 1980

Discrete series for semisimple symmetric spaces

  • M. FLENSTED-JENSEN
  • Ann. Math
  • 1980
1 Excerpt

Eigenspaces of invariant differential operators on an affine symmetric space

  • T. OSrnMA, J. SEKIGUCnl
  • Invent. Math
  • 1980

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