q-Selberg integrals and Macdonald polynomials
Kaneko, Jyoichi
Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996), p. 583-637 / Harvested from Numdam
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@article{ASENS_1996_4_29_5_583_0,
     author = {Kaneko, Jyoichi},
     title = {$q$-Selberg integrals and Macdonald polynomials},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {29},
     year = {1996},
     pages = {583-637},
     doi = {10.24033/asens.1749},
     mrnumber = {98k:33026},
     zbl = {0910.33011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1996_4_29_5_583_0}
}

Kaneko, Jyoichi. $q$-Selberg integrals and Macdonald polynomials. Annales scientifiques de l'École Normale Supérieure, Tome 29 (1996) pp. 583-637. doi : 10.24033/asens.1749. http://gdmltest.u-ga.fr/item/ASENS_1996_4_29_5_583_0/

[An] G. E. Andrews, q-Series, CBMS Regional Conference Series in Math. (American Mathematical Society, Providence, RI, 1986).

[Ao1] K. Aomoto, On connection coefficients for q-difference systems of A-type Jackson integrals (SIAM. J. Math. Anal., Vol. 25, 1994, pp. 256-273). | MR 96f:33041 | Zbl 0794.33011

[Ao2] K. Aomoto, On product formulae for Jackson integrals associated with root systems, preprint, 1994.

[Ao3] K. Aomoto, On a theta product formula for the symmetric A-type connection function (Osaka J. Math., Vol. 32, 1995, pp. 35-39). | MR 96d:33010 | Zbl 0822.33011

[As1] R. Askey, The q-gamma and q-beta functions (Applicable Analysis, Vol. 8, 1978, pp. 125-141). | MR 80h:33003 | Zbl 0398.33001

[As2] R. Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews (SIAM. J. Math. Anal., Vol. 11, 1980, pp. 938-951). | MR 82e:33002 | Zbl 0458.33002

[BC] D. Barsky and M. Carpentier, Intégrales de Selberg généralisées, preprint, 1994.

[BO] R. J. Beerends and E. M. Opdam, Certain hypergeometric series related to the root system BC (Trans. Amer. Math. Soc., Vol. 339, 1993, pp. 581-610). | MR 94e:33024 | Zbl 0794.33009

[C] S. Cooper, Proof of a q-extension of a conjecture of Forrester, preprint, 1994.

[F] P. J. Forrester, Some multidimensional integrals related to many body systems with the 1/r² potential (J. Phys. A, Vol. 25, 1992, L607-L614). | MR 93a:81057 | Zbl 0768.33015

[GR] G. Gasper and M. Rahman, Basic hypergeometric functions (Cambridge University Press, London, 1990).

[H] L. Habsieger, Une q-intégrale de Selberg et Askey (SIAM J. Math. Anal., Vol. 19, 1988, pp. 1475-1489). | MR 89m:33002 | Zbl 0664.33001

[Kad1] K. Kadell, A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris (SIAM J. Math. Anal., Vol. 19, 1988, pp. 969-986). | MR 89h:33006b | Zbl 0643.33004

[Kad2] K. Kadell, The Selberg-Jack symmetric functions (to appear in Adv. in Math.). | Zbl 0885.33009

[Kan1] J. Kaneko, Selberg integrals and hypergeometric functions (in Special Differential Equations, Proc. of the Taniguchi Workshops, Kyushu University, 1992, pp. 62-68).

[Kan2] J. Kaneko, Selberg integrals and hypergeometric functions associated with Jack polynomials (SIAM J. Math. Anal., Vol. 24, 1993, pp. 1086-1110). | MR 94h:33010 | Zbl 0783.33008

[Kan3] J. Kaneko, Constant term identities of Forrester-Zeilberger-Cooper (to appear in Discrete Math.). | Zbl 0884.33012

[Ko] A. Korányi, Hua-type integrals, hypergeometric functions and symmetric polynomials, (in International symposium in memory of Hua Loo Keng, Vol. 2, Analysis, S. GONG et al., eds., Science Press, Beijing and Springer-Verlag, Berlin, 1991, pp. 169-180). | MR 92h:33036 | Zbl 0814.33009

[L] M. Lassalle, Une formule du binôme généralisée pour les polynômes de Jack (C. R. Acad. Sci. Paris, Sér. I Math., Vol. 310, 1990, pp. 253-256). | MR 91c:05193 | Zbl 0698.33010

[Ma1] I. G. Macdonald, Symmetric Functions and Hall Polynomials, (Oxford University Press, Oxford, 1979). | MR 84g:05003 | Zbl 0487.20007

[Ma2] I. G. Macdonald, A new class of symmetric functions (Actes 20e Séminaire Lotharingien, Publ. I.R.M.A. Strasbourg, 1988, pp. 131-171).

[Ma3] I. G. Macdonald, manuscript of second edition of [Ma1].

[Z] D. Zeilberger, Proof of a q-analog of a constant term identity conjectured by Forrester (J. Comb. Theory Ser. A, Vol. 66, 1994, pp. 311-312). | MR 95f:05016 | Zbl 0809.05013