Dunkl operators

G. J. Heckman

Séminaire Bourbaki (1996-1997)

  • Volume: 39, page 223-246
  • ISSN: 0303-1179

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Heckman, G. J.. "Dunkl operators." Séminaire Bourbaki 39 (1996-1997): 223-246. <http://eudml.org/doc/110230>.

@article{Heckman1996-1997,
author = {Heckman, G. J.},
journal = {Séminaire Bourbaki},
keywords = {Dunkl operators},
language = {eng},
pages = {223-246},
publisher = {Société Mathématique de France},
title = {Dunkl operators},
url = {http://eudml.org/doc/110230},
volume = {39},
year = {1996-1997},
}

TY - JOUR
AU - Heckman, G. J.
TI - Dunkl operators
JO - Séminaire Bourbaki
PY - 1996-1997
PB - Société Mathématique de France
VL - 39
SP - 223
EP - 246
LA - eng
KW - Dunkl operators
UR - http://eudml.org/doc/110230
ER -

References

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  1. [BS] E.P. van den Ban and H. Schlichtkrull, The most continuous part of the Plancherel decomposition for a reductive symmetric space, Ann. Math. (to appear). Zbl0878.43018
  2. [BHO] R. Brussee, G.J. Heckman and E.M. Opdam, Variation on a theme of Macdonald, Math Z.208 (1991), 1-10. Zbl0763.33006MR1125728
  3. [Ca] R.W. Carter, Finite groups of Lie type, Wiley, New York, 1985. Zbl0567.20023MR794307
  4. [Ch1] I. Cherednik, A unification of Knizhnik-Zamolodchikov equations and Dunkl operators via affine Hecke algebras, Invent. Math.106 (1991), 411-432. Zbl0725.20012MR1128220
  5. [Ch2] I. Cherednik, Integration of quantum many body problems by affine Knizhnik-Zamolodchikov equations, Adv. in Math.106 (1994), 65-95. Zbl0806.35146MR1275866
  6. [Ch3] I. Cherednik,Double affine Hecke algebras and Macdonald's conjectures, Ann. Math.141 (1995), 191-216. Zbl0822.33008MR1314036
  7. [Ch4] I. Cherednik, Macdonald's evaluation conjectures and difference Fourier transform, Invent. Math.122 (1995), 119-145. Zbl0854.22021MR1354956
  8. [De] P. Deligne, Équations différentielles à points singuliers réguliers, Lect. Notes Math.163, 1970. Zbl0244.14004MR417174
  9. [Dr] V.G. Drinfeld, Degenerate affine Hecke algebras and Yangians, Funct. Anal. Appl.20 (1986), 58-60. Zbl0599.20049MR831053
  10. [Du1] C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc.311 (1989), 167-183. Zbl0652.33004MR951883
  11. [Du2] C.F. Dunkl, Hankl transforms associated to finite reflection groups, Contemp. Math.138 (1992), 123-138. Zbl0789.33008MR1199124
  12. [GR] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge Univ. Press, 1990. Zbl0695.33001MR1052153
  13. [He1] G.J. Heckman, Root systems and hypergeometric functions II, Comp. Math.64 (1987), 353-373. Zbl0656.17007MR918417
  14. [He2] G.J. Heckman, An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math.103 (1991), 341-350. Zbl0721.33009MR1085111
  15. [HO1] G.J. Heckman and E.M. Opdam, Root systems and hypergeometric functions I, Comp. Math.64 (1987), 329-352. Zbl0656.17006MR918416
  16. [HO2] G.J. Heckman and E.M. Opdam, Yang's system of particles and Hecke algebras, Ann. Math.145 (1997), 139-173. Zbl0873.43007MR1432038
  17. [HO3] G.J. Heckman and E.M. Opdam, Harmonic analysis for affine Hecke algebras, Current Developments in Mathematics, 1996, Intern. Press, Boston. Zbl0932.22006MR1724944
  18. [HS] G.J. Heckman and H. Schlichtkrull, Harmonic Analysis and Special Functions on Symmetric Spaces, Persp. in Math.16, Acad. Press, 1994. Zbl0836.43001MR1313912
  19. [Hel] S. Helgason, Groups and Geometric Analysis, Acad. Press, New York, 1984. Zbl0543.58001MR754767
  20. [J] M.F.E. de Jeu, The Dunkl transform, Invent. Math.113 (1993), 147-162. Zbl0789.33007MR1223227
  21. [KL] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math.87 (1987), 153-215. Zbl0613.22004MR862716
  22. [Lo] E. Looijenga, Arrangements, KZ systems and Lie algebra homology, Comm. Math. Inst. Utrecht Univ.18 (1994), 105-124. MR1709348
  23. [Lu] G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc.2 (1989), 599-695. Zbl0715.22020MR991016
  24. [Ma1] I.G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal.13 (1982), 988-1007. Zbl0498.17006MR674768
  25. [Ma2] I.G. Macdonald, Orthogonal polynomials associated with root systems, preprint (1988). MR1100299
  26. [Ma3] I.G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Sém. Bourbaki no 797, 1995. Zbl0883.33008MR1423624
  27. [Ma4] I.G. Macdonald, Symmetric Functions and Hall polynomials, 2nd edition, Oxford Univ. Press, 1995. Zbl0899.05068MR1354144
  28. [Ma5] I.G. Macdonald, Symmetric Functions and Orthogonal Polynomials (Postscript), preprint (1996). MR1488699
  29. [Mat] A. Matsuo, Integrable connections related to zonal spherical functions, Invent. Math.110 (1992), 95-121. Zbl0801.35131MR1181818
  30. [MW] C. Moeglin and J.L. Waldspurger, Décomposition Spectrale et Séries d'Eisentein, Prog. in Math.113, Birkhäuser, 1994. Zbl0794.11022MR1261867
  31. [Mo] J. Moser, Three integrable Hamiltonian systems connected with isospectral deformation, Adv. in Math.16 (1975), 197-220. Zbl0303.34019MR375869
  32. [OP] M.A. Olshanetsky and A.M. Perelomov, Completely integrable Hamiltonian systems connected with semisimple Lie algebras, Invent. Math.37 (1976), 93-108. Zbl0342.58017MR426053
  33. [O1] E.M. Opdam, Root systems and hypergeometric functions III, Comp. Math.67 (1988), 21-49. Zbl0669.33007MR949270
  34. [O2] E.M. Opdam, Root systems and hypergeometric functions IV, Comp. Math.67 (1988), 191-209. Zbl0669.33008MR951750
  35. [O3] E.M. Opdam, Some applications of hypergeometric shift operators, Invent. Math.98 (1989), 1-18. Zbl0696.33006MR1010152
  36. [04] E.M. Opdam, An analogue of the Gauss summation formula for hypergeometric functions related to root systems, Math. Z.212 (1993), 313-336. Zbl0789.33009MR1207296
  37. [05] E.M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math.175 (1995), 75-121. Zbl0836.43017MR1353018
  38. [O6] E.M. Opdam, Cuspidal hypergeometric functions, preprint (1996). MR1803882
  39. [Ru] S.N.M. Ruijsenaars, Complete integrability of relativistic Calogero-Moser systems and elliptic function identities, Comm. Math. Phys.110 (1987), 191-213. Zbl0673.58024MR887995

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