q -Selberg integrals and Macdonald polynomials

Jyoichi Kaneko

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 5, page 583-637
  • ISSN: 0012-9593

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Kaneko, Jyoichi. "$q$-Selberg integrals and Macdonald polynomials." Annales scientifiques de l'École Normale Supérieure 29.5 (1996): 583-637. <http://eudml.org/doc/82418>.

@article{Kaneko1996,
author = {Kaneko, Jyoichi},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {-Selberg integral; Macdonald polynomials},
language = {eng},
number = {5},
pages = {583-637},
publisher = {Elsevier},
title = {$q$-Selberg integrals and Macdonald polynomials},
url = {http://eudml.org/doc/82418},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Kaneko, Jyoichi
TI - $q$-Selberg integrals and Macdonald polynomials
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 5
SP - 583
EP - 637
LA - eng
KW - -Selberg integral; Macdonald polynomials
UR - http://eudml.org/doc/82418
ER -

References

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  2. [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). Zbl0794.33011MR96f:33041
  3. [Ao2] K. AOMOTO, On product formulae for Jackson integrals associated with root systems, preprint, 1994. 
  4. [Ao3] K. AOMOTO, On a theta product formula for the symmetric A-type connection function (Osaka J. Math., Vol. 32, 1995, pp. 35-39). Zbl0822.33011MR96d:33010
  5. [As1] R. ASKEY, The q-gamma and q-beta functions (Applicable Analysis, Vol. 8, 1978, pp. 125-141). Zbl0398.33001MR80h:33003
  6. [As2] R. ASKEY, Some basic hypergeometric extensions of integrals of Selberg and Andrews (SIAM. J. Math. Anal., Vol. 11, 1980, pp. 938-951). Zbl0458.33002MR82e:33002
  7. [BC] D. BARSKY and M. CARPENTIER, Intégrales de Selberg généralisées, preprint, 1994. 
  8. [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). Zbl0794.33009MR94e:33024
  9. [C] S. COOPER, Proof of a q-extension of a conjecture of Forrester, preprint, 1994. 
  10. [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). Zbl0768.33015MR93a:81057
  11. [GR] G. GASPER and M. RAHMAN, Basic hypergeometric functions (Cambridge University Press, London, 1990). Zbl0695.33001
  12. [H] L. HABSIEGER, Une q-intégrale de Selberg et Askey (SIAM J. Math. Anal., Vol. 19, 1988, pp. 1475-1489). Zbl0664.33001MR89m:33002
  13. [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). Zbl0643.33004MR89h:33006b
  14. [Kad2] K. KADELL, The Selberg-Jack symmetric functions (to appear in Adv. in Math.). Zbl0885.33009
  15. [Kan1] J. KANEKO, Selberg integrals and hypergeometric functions (in Special Differential Equations, Proc. of the Taniguchi Workshops, Kyushu University, 1992, pp. 62-68). 
  16. [Kan2] J. KANEKO, Selberg integrals and hypergeometric functions associated with Jack polynomials (SIAM J. Math. Anal., Vol. 24, 1993, pp. 1086-1110). Zbl0783.33008MR94h:33010
  17. [Kan3] J. KANEKO, Constant term identities of Forrester-Zeilberger-Cooper (to appear in Discrete Math.). Zbl0884.33012
  18. [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). Zbl0814.33009MR92h:33036
  19. [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). Zbl0698.33010MR91c:05193
  20. [Ma1] I. G. MACDONALD, Symmetric Functions and Hall Polynomials, (Oxford University Press, Oxford, 1979). Zbl0487.20007MR84g:05003
  21. [Ma2] I. G. MACDONALD, A new class of symmetric functions (Actes 20e Séminaire Lotharingien, Publ. I.R.M.A. Strasbourg, 1988, pp. 131-171). 
  22. [Ma3] I. G. MACDONALD, manuscript of second edition of [Ma1]. 
  23. [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). Zbl0809.05013MR95f:05016

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