Skip to main content
Log in

Harmonic analysis for certain representations of graded Hecke algebras

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ban van den, E.P. & Schlichtkrull, H., The most continuous part of the Plancherel decomposition for a reductive symmetric space. To appear.

  2. Cherednik I., A unification of Knizhnik-Zamolodchikov equations and Dunkl operators via affine Hecke algebras.Invent. Math. 106 (1991), 411–432.

    Article  MATH  MathSciNet  Google Scholar 

  3. —, Intergration of quantum many-body problems by affine Knizhnik-Zamolodchikov equations.Adv. in Math., 106 (1994), 65–95.

    Article  MATH  MathSciNet  Google Scholar 

  4. — The Macdonald constant-term conjecture.Internat. Math. Res. Notices, 6 (1993), 165–177.

    Article  MATH  MathSciNet  Google Scholar 

  5. Dunkl, C.F., Differential-difference operators associated to reflection groupsTrans. Amer. Math. Soc., 311 (1989), 167–183.

    Article  MATH  MathSciNet  Google Scholar 

  6. Heckman, G.J., Root systems and hypergeometric functions II.Compositio Math., 64 (1987), 353–374.

    MATH  MathSciNet  Google Scholar 

  7. —, An elementary approach to the hypergeometric shift operators of Opdam.Invent. Math., 103 (1991), 341–350.

    Article  MATH  MathSciNet  Google Scholar 

  8. Heckman, G.J. Self adjoint triangular operators are commutative. Unpublished manuscript, 1991.

  9. Heckman, G.J. Lectures on Hypergeometric and Spherical Functions. Notes for the European School of Group Theory. Luminy, 1991.

  10. Heckman, G.J. &Opdam, E.M., Root systems and hypergeometric functions I.Compositio Math., 64 (1987), 329–352.

    MathSciNet  Google Scholar 

  11. Helgason, S.,Groups and Geometric Analysis. Academic Press, New York-London, 1984.

    Google Scholar 

  12. Hörmander, L.,The Analysis of Linear Partial Differential Operators I. Grundlehren Math. Wiss. 256. Springer-Verlag, Berlin-New York, 1983.

    Google Scholar 

  13. Jeu de, M.F.E., The Dunkl transform.Invent. Math., 113 (1993), 147–162.

    Article  MATH  MathSciNet  Google Scholar 

  14. Koornwinder, T.H., A new proof of a Paley-Wiener type thoorem for the Jacobi transform.Ark. Mat., 13 (1975), 145–159.

    Article  MATH  MathSciNet  Google Scholar 

  15. Lusztig, G., Affine Hecke algebras and their graded version.J. Amer. Math. Soc., 2 (1989), 599–685.

    Article  MATH  MathSciNet  Google Scholar 

  16. Macdonald, I.G., The Poincaré series of a Coxeter group.Math. Ann., 199 (1972), 161–174.

    Article  MATH  MathSciNet  Google Scholar 

  17. —, Some conjectures for root systems.SIAM J. Math. Anal., 13 (1982), 988–1007.

    Article  MATH  MathSciNet  Google Scholar 

  18. —, Orthogonal polynomials associated with root systems, inOrthogonal Polynomials: Theory and Practice (Columbus, Ohio, 1989), pp. 311–318. NATO Adv. Sci. Inst. Ser. C, 294. Kluwer, Dordrecht, 1990.

    Google Scholar 

  19. Matsuo, A., Integrable connections related to zonal spherical functions.Invent. Math., 110 (1992), 95–121.

    Article  MATH  MathSciNet  Google Scholar 

  20. Opdam, E.M., Some applications of hypergeometric shift operators.Invent. Math. 98 (1989), 1–18.

    Article  MATH  MathSciNet  Google Scholar 

  21. —, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group.Compositio Math., 85 (1993), 333–373.

    MATH  MathSciNet  Google Scholar 

  22. —, An analogue of the Gauss summation formula for hypergeometric functions related to root systems.Math. Z., 212 (1993), 313–336.

    MATH  MathSciNet  Google Scholar 

  23. Peetre, J., Rectification à l'article “Une caractérisation abstraite des opérateurs différentiels”.Math. Scand., 8 (1960), 116–120.

    MATH  MathSciNet  Google Scholar 

  24. Rogawski, J.D., On modules over the Hecke algebra of ap-adic group.Invent. Math., 79 (1985), 443–465.

    Article  MATH  MathSciNet  Google Scholar 

  25. Rosenberg, J., A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group.Proc. Amer. Math. Soc., 63 (1977), 143–149.

    Article  MATH  MathSciNet  Google Scholar 

  26. Varadarajan, V.S.,Lie Groups, Lie Algebras and Their Representations. Graduate Texts in Math., 102. Springer-Verlag, New York-Berlin, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Opdam, E.M. Harmonic analysis for certain representations of graded Hecke algebras. Acta Math. 175, 75–121 (1995). https://doi.org/10.1007/BF02392487

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392487

Keywords

Navigation