Dunkl operators
Séminaire Bourbaki : volume 1996/97, exposés 820-834, Astérisque, no. 245 (1997), Talk no. 828, 24 p.
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Heckman, G. J. Dunkl operators, in Séminaire Bourbaki : volume 1996/97, exposés 820-834, Astérisque, no. 245 (1997), Talk no. 828, 24 p. http://archive.numdam.org/item/SB_1996-1997__39__223_0/

[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). | Zbl

[BHO] R. Brussee, G. J. Heckman and E. M. Opdam, Variation on a theme of Macdonald, Math Z. 208 (1991), 1-10. | DOI | EuDML | MR | Zbl

[Ca] R. W. Carter, Finite groups of Lie type, Wiley, New York, 1985. | MR | Zbl

[Ch1] I. Cherednik, A unification of Knizhnik-Zamolodchikov equations and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), 411-432. | DOI | EuDML | MR | Zbl

[Ch2] I. Cherednik, Integration of quantum many body problems by affine Knizhnik-Zamolodchikov equations, Adv. in Math. 106 (1994), 65-95. | DOI | MR | Zbl

[Ch3] I. Cherednik,Double affine Hecke algebras and Macdonald's conjectures, Ann. Math. 141 (1995), 191-216. | DOI | MR | Zbl

[Ch4] I. Cherednik, Macdonald's evaluation conjectures and difference Fourier transform, Invent. Math. 122 (1995), 119-145. | DOI | EuDML | MR | Zbl

[De] P. Deligne, Équations différentielles à points singuliers réguliers, Lect. Notes Math. 163, 1970. | MR | Zbl

[Dr] V. G. Drinfeld, Degenerate affine Hecke algebras and Yangians, Funct. Anal. Appl. 20 (1986), 58-60. | DOI | MR | Zbl

[Du1] C. F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), 167-183. | DOI | MR | Zbl

[Du2] C. F. Dunkl, Hankl transforms associated to finite reflection groups, Contemp. Math. 138 (1992), 123-138. | DOI | MR | Zbl

[GR] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge Univ. Press, 1990. | MR | Zbl

[He1] G. J. Heckman, Root systems and hypergeometric functions II, Comp. Math. 64 (1987), 353-373. | EuDML | Numdam | MR | Zbl

[He2] G. J. Heckman, An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math. 103 (1991), 341-350. | DOI | EuDML | MR | Zbl

[HO1] G. J. Heckman and E. M. Opdam, Root systems and hypergeometric functions I, Comp. Math. 64 (1987), 329-352. | EuDML | Numdam | MR | Zbl

[HO2] G. J. Heckman and E. M. Opdam, Yang's system of particles and Hecke algebras, Ann. Math. 145 (1997), 139-173. | DOI | MR | Zbl

[HO3] G. J. Heckman and E. M. Opdam, Harmonic analysis for affine Hecke algebras, Current Developments in Mathematics, 1996, Intern. Press, Boston. | MR | Zbl

[HS] G. J. Heckman and H. Schlichtkrull, Harmonic Analysis and Special Functions on Symmetric Spaces, Persp. in Math. 16, Acad. Press, 1994. | MR | Zbl

[Hel] S. Helgason, Groups and Geometric Analysis, Acad. Press, New York, 1984. | MR | Zbl

[J] M. F. E. De Jeu, The Dunkl transform, Invent. Math. 113 (1993), 147-162. | DOI | EuDML | MR | Zbl

[KL] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), 153-215. | DOI | EuDML | MR | Zbl

[Lo] E. Looijenga, Arrangements, KZ systems and Lie algebra homology, Comm. Math. Inst. Utrecht Univ. 18 (1994), 105-124. | MR | Zbl

[Lu] G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), 599-695. | DOI | MR | Zbl

[Ma1] I.G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 988-1007. | DOI | MR | Zbl

[Ma2] I. G. Macdonald, Orthogonal polynomials associated with root systems, preprint (1988). | MR | Zbl

[Ma3] I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Sém. Bourbaki no 797, 1995. | EuDML | Numdam | MR | Zbl

[Ma4] I. G. Macdonald, Symmetric Functions and Hall polynomials, 2nd edition, Oxford Univ. Press, 1995. | MR | Zbl

[Ma5] I. G. Macdonald, Symmetric Functions and Orthogonal Polynomials (Postscript), preprint (1996). | MR | Zbl

[Mat] A. Matsuo, Integrable connections related to zonal spherical functions, Invent. Math. 110 (1992), 95-121. | DOI | EuDML | MR | Zbl

[MW] C. Moeglin and J. L. Waldspurger, Décomposition Spectrale et Séries d'Eisentein, Prog. in Math. 113, Birkhäuser, 1994. | MR | Zbl

[Mo] J. Moser, Three integrable Hamiltonian systems connected with isospectral deformation, Adv. in Math. 16 (1975), 197-220. | DOI | MR | Zbl

[OP] M. A. Olshanetsky and A. M. Perelomov, Completely integrable Hamiltonian systems connected with semisimple Lie algebras, Invent. Math. 37 (1976), 93-108. | DOI | EuDML | MR | Zbl

[O1] E. M. Opdam, Root systems and hypergeometric functions III, Comp. Math. 67 (1988), 21-49. | EuDML | Numdam | MR | Zbl

[O2] E. M. Opdam, Root systems and hypergeometric functions IV, Comp. Math. 67 (1988), 191-209. | EuDML | Numdam | MR | Zbl

[O3] E. M. Opdam, Some applications of hypergeometric shift operators, Invent. Math. 98 (1989), 1-18. | DOI | EuDML | MR | Zbl

[04] E. M. Opdam, An analogue of the Gauss summation formula for hypergeometric functions related to root systems, Math. Z. 212 (1993), 313-336. | DOI | EuDML | MR | Zbl

[05] E. M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121. | DOI | MR | Zbl

[O6] E. M. Opdam, Cuspidal hypergeometric functions, preprint (1996). | MR | Zbl

[Ru] S. N. M. Ruijsenaars, Complete integrability of relativistic Calogero-Moser systems and elliptic function identities, Comm. Math. Phys. 110 (1987), 191-213. | DOI | MR | Zbl