Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group
Opdam, E. M.
Compositio Mathematica, Tome 89 (1993), p. 333-373 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{CM_1993__85_3_333_0,
     author = {Opdam, E. M.},
     title = {Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {333-373},
     mrnumber = {1214452},
     zbl = {0778.33009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__85_3_333_0}
}

Opdam, E. M. Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group. Compositio Mathematica, Tome 89 (1993) pp. 333-373. http://gdmltest.u-ga.fr/item/CM_1993__85_3_333_0/

[1] Bott, R.: An application of the Morse theory to the topology of Lie groups. Bull Soc. Math. France 84 (1958), 251-282. | Numdam | MR 87035 | Zbl 0073.40001

[2] Bourbaki, N.: Algèbre, Chapitre 9. Hermann, Paris, 1959. | Zbl 0102.25503

[3] Bourbaki, N.: Groupes et Algèbres de Lie, Chapitres 4, 5 et 6. Hermann, Paris, 1968. | MR 240238

[4] Brieskorn, E.: Die fundamentalgruppe des Raumes der regulären orbits einer komplexen spiegelungsgruppe. Inv. Math. 12 (1971), 57-61. | MR 293615 | Zbl 0204.56502

[5] Curtis, C.W., Iwahori, N. and Kilmoyer, R.W.: Hecke algebras and the characters of parabolic type of finite groups with BN-pairs. Publ. Math. IHES 40 (1971), 81-116. | Numdam | MR 347996 | Zbl 0254.20004

[6] Deligne, P.: Equations Differentielles à Points Singulier Regulier. LNM 163, Springer-Verlag (1970). | MR 417174 | Zbl 0244.14004

[7] Deligne, P.: Les immeubles des groupes de tresses généraliser. Inv. Math. 17 (1972), 273-302. | MR 422673 | Zbl 0238.20034

[8] Dunkl, C.F.: Differential-difference operators associated to reflection groups. Trans. Amer. Math. Soc. 311(1) (1989). | MR 951883 | Zbl 0652.33004

[9] Dunkl, C.F.: Harmonic polynomials and peak sets of reflection groups. Geom. Dedicata 32 (1989), 157-171. | MR 1029672 | Zbl 0685.33012

[10] Dunkl, C.F.: Operators Commuting with Coxeter Group Actions on Polynomials, in D. Stanton (ed.) Invariant Theory and Tableaux. Springer-Verlag (1990). | MR 1035491 | Zbl 0719.33008

[11] Dunkl, C.F.: Integral kernels with reflection group invariance. Canad. J. Math. (to appear). | MR 1145585 | Zbl 0827.33010

[12] Dunkl, C.F.: Hankel transforms associated to finite reflection groups (to appear). | MR 1199124

[13] Gyoja, A. and Uno, K.: On the semisimplicity of Hecke algebras. J. Math Soc. Japan 41(1) (1989). | MR 972165 | Zbl 0647.20038

[14] Harish-Chandra: Spherical functions on a semisimple Lie group I. Amer. J. Math. 80 (1958), 241-310. | MR 94407 | Zbl 0093.12801

[15] Harish-Chandra: Spherical functions on a semisimple Lie group II. Amer. J. Math. 80 (1958), 553-613. | MR 101279 | Zbl 0093.12801

[16] Heckman, G.J.: Root systems and hypergeometric functions II. Compositio Math. 64 (1987), 353-374. | Numdam | MR 918417 | Zbl 0656.17007

[17] Heckman, G.J.: A remark on the Dunkl differential-difference operators. Proc. of the Bowdoin conference on harmonic analysis on reductive groups, 1989. | Zbl 0749.33005

[18] Heckman, G.J.: An elementary approach to the hypergeometric shift operators of Opdam. Inv. Math. 103 (1991), 341-350. | MR 1085111 | Zbl 0721.33009

[19] Heckman, G.J. and Opdam, E.M.: Root systems and hypergeometric functions I. Compositio Math. 64 (1987), 329-352. | Numdam | MR 918416 | Zbl 0656.17006

[20] Helgason, S.: Groups and Geometric Analysis. Academic Press (1984). | MR 754767 | Zbl 0543.58001

[21] Katz, N.M.: Nilpotent connections and the monodromy theorem; application of a result of Turrittin. Publ. Math. I.H.E.S. 39 (1970), 355-432. | Numdam | MR 291177 | Zbl 0221.14007

[22] Lek, H. V.D.: The homotopy type of complex hyperplane complements. Thesis, Univ. of Nijmegen, 1983.

[23] Macdonald, I.G.: The Poincaré series of a Coxeter group. Math. Ann. 199 (1972), 161-174. | MR 322069 | Zbl 0286.20062

[24] Macdonald, I.G.: Some conjectures for root systems. SIAM J. Math. An. 13 (1982) 988-1007. | MR 674768 | Zbl 0498.17006

[25] Matsuo, A.: Knizhnik-Zamolodchikov type equations and zonal spherical functions. Res. Inst. Math. Sci. 750, Kyoto University (1991).

[26] Opdam, E.M.: Root systems and hypergeometric functions III. Compositio Math. 67 (1988), 21-49. | Numdam | MR 949270 | Zbl 0669.33007

[27] Opdam, E.M.: Root systems and hypergeometric functions IV. Compositio Math. 67 (1988), 191-209. | Numdam | MR 951750 | Zbl 0669.33008

[28] Opdam, E.M.: Some applications of hypergeometric shift operators. Inv. Math. 98 (1989), 1-18. | MR 1010152 | Zbl 0696.33006

[29] Solomon, L.: The orders of finite Chevalley groups. J. Algebra 3 (1966), 376-393. | MR 199275 | Zbl 0151.02003

[30] Springer, T.A.: Regular elements of finite reflection groups. Inv. Math. 25 (1974), 159-198. | MR 354894 | Zbl 0287.20043

[31] Stanley, R.: Relative invariants of finite groups generated by pseudoreflections. J. Algebra 49 (1977), 134-148. | MR 460484 | Zbl 0383.20029

[32] Steinberg, R.: Lecture on Chevalley Groups. Lecture notes, Yale Univ. (1967). | MR 466335 | Zbl 1196.22001

[33] Varadarajan, V.S.: Lie Groups, Lie Algebras and their Representations, G.T.M., Springer-Verlag (1974). | MR 376938 | Zbl 0371.22001 | Zbl 0955.22500

[34] Walter, W.: Gewöhnliche Differentialgleichungen. Heidelberger Taschenbücher, Springer-Verlag (1972). | MR 404728 | Zbl 0247.34001

[35] Yano, T. and Sekiguchi, J.: The microlocal structure of weighted homogeneous polynomials associated with Coxeter systems I. Tokyo J. Math. 2 (1979). | MR 560265 | Zbl 0449.58025