@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}, pages = {583--637}, publisher = {Elsevier}, volume = {Ser. 4, 29}, number = {5}, year = {1996}, doi = {10.24033/asens.1749}, mrnumber = {98k:33026}, zbl = {0910.33011}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.1749/} }
TY - JOUR AU - Kaneko, Jyoichi TI - $q$-Selberg integrals and Macdonald polynomials JO - Annales scientifiques de l'École Normale Supérieure PY - 1996 SP - 583 EP - 637 VL - 29 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.24033/asens.1749/ DO - 10.24033/asens.1749 LA - en ID - ASENS_1996_4_29_5_583_0 ER -
Kaneko, Jyoichi. $q$-Selberg integrals and Macdonald polynomials. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 5, pp. 583-637. doi : 10.24033/asens.1749. http://www.numdam.org/articles/10.24033/asens.1749/
[An] q-Series, CBMS Regional Conference Series in Math. (American Mathematical Society, Providence, RI, 1986).
,[Ao1] On connection coefficients for q-difference systems of A-type Jackson integrals (SIAM. J. Math. Anal., Vol. 25, 1994, pp. 256-273). | MR | Zbl
,[Ao2] On product formulae for Jackson integrals associated with root systems, preprint, 1994.
,[Ao3] On a theta product formula for the symmetric A-type connection function (Osaka J. Math., Vol. 32, 1995, pp. 35-39). | MR | Zbl
,[As1] The q-gamma and q-beta functions (Applicable Analysis, Vol. 8, 1978, pp. 125-141). | MR | Zbl
,[As2] Some basic hypergeometric extensions of integrals of Selberg and Andrews (SIAM. J. Math. Anal., Vol. 11, 1980, pp. 938-951). | MR | Zbl
,[BC] Intégrales de Selberg généralisées, preprint, 1994.
and ,[BO] Certain hypergeometric series related to the root system BC (Trans. Amer. Math. Soc., Vol. 339, 1993, pp. 581-610). | MR | Zbl
and ,[C] Proof of a q-extension of a conjecture of Forrester, preprint, 1994.
,[F] Some multidimensional integrals related to many body systems with the 1/r² potential (J. Phys. A, Vol. 25, 1992, L607-L614). | MR | Zbl
,[GR] Basic hypergeometric functions (Cambridge University Press, London, 1990).
and ,[H] Une q-intégrale de Selberg et Askey (SIAM J. Math. Anal., Vol. 19, 1988, pp. 1475-1489). | MR | Zbl
,[Kad1] 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 | Zbl
,[Kad2] The Selberg-Jack symmetric functions (to appear in Adv. in Math.). | Zbl
,[Kan1] Selberg integrals and hypergeometric functions (in Special Differential Equations, Proc. of the Taniguchi Workshops, Kyushu University, 1992, pp. 62-68).
,[Kan2] Selberg integrals and hypergeometric functions associated with Jack polynomials (SIAM J. Math. Anal., Vol. 24, 1993, pp. 1086-1110). | MR | Zbl
,[Kan3] Constant term identities of Forrester-Zeilberger-Cooper (to appear in Discrete Math.). | Zbl
,[Ko] 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 | Zbl
,[L] 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 | Zbl
,[Ma1] Symmetric Functions and Hall Polynomials, (Oxford University Press, Oxford, 1979). | MR | Zbl
,[Ma2] A new class of symmetric functions (Actes 20e Séminaire Lotharingien, Publ. I.R.M.A. Strasbourg, 1988, pp. 131-171).
,[Ma3]
, manuscript of second edition of [Ma1].[Z] 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 | Zbl
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