Symmetry Classification for Jackson Integrals Associated with the Root System BCn

Compositio Mathematica

Volumn 136, Issue 2, 2003, Pages 209-216

  Ito, Masahiko ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Bailey's very well poised 6 6 sum; Gustafson's Cn type sum; Jackson integrals; Non reduced root system; Van Diejen's BCn type sum

Indexed keywords

EID: 0347126794     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022892011301     Document Type: Article

References (24)

1. [Ao1] Aomoto, K.: On elliptic product formulas for Jackson integrals associated with reduced root systems, J. Algebraic Combin. 8 (1998), 115-126.
2. [Ao2] Aomoto, K.: Connection formulas in the q-analog de Rham cohomology, In: Functional Analysis on the Eve of the 21st Century, Vol. 1 (New Brunswick, NJ, 1993), Progr. in Math. 131, Birkhäuser, Boston, 1995, pp. 1-12.
3. [AW] Askey, R. and Wilson, J.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54, 1985.
4. [Ba] Bailey, W. N.: Series of hypergeometric type which are infinite in both directions, Quart. J. Math. 71 (1936), 105-115.
5. [Bo] Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris, 1969.
6. [C1] Cherednik, I.: Double affine Hecke algebras and Macdonald's conjectures, Ann. of Math. (2) 141 (1995), 191-216.
7. [C2] Cherednik, I.: Intertwining operators of double affine Hecke algebra, Selecta Math. (N.S.) 3 (1997), 459-495.
8. [vD] van Diejen, J. F.: On certain multiple Bailey, Rogers and Dougall type summation Formulas, Publ. RIMS, Kyoto Univ. 33 (1997), 483-508.
9. [vDV] van Diejen, J. F. and Vinet, L.: The quantum dynamics of the compactified trigonometric Ruijsenaar-Schneider model, Comm. Math. Phys. 197 (1998), 33-74.
10. [GR] Gasper, G. and Rahman, M.: Basic Hypergeometric Series, Encycl. Math. Appl. 35, Cambridge Univ. Press, 1990.
11. [Gu1] Gustafson, R. A.: The Macdonald identities for affine root systems of classical type and hypergeometric series very-well-poised on semisimple Lie algebras, Ramanujan International Symposium on Analysis (Pune, 1987), Macmillan of India, New Delhi, 1989, pp. 185-224.
12. [Gu2] Gustafson, R. A.: A generalization of Selberg's beta integral, Bull. Amer. Math. Soc. 22 (1990), 97-105.
13. [Gu3] Gustafson, R. A.: Some q-Beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras, Trans. Amer. Math. Anal. 23 (1992), 552-561.
14. [Gu4] Gustafson, R.A.: Some q-Beta integrals on SU(n) and Sp(n) that generalize the Askey-Wilson and Nasrallah-Rahman integral, SIAM J. Math. Anal. 25 (1994), 441-449.
15. [Ito1] Ito, M.: On a theta product formula for Jackson integrals associated with root system of rank two, J. Math. Anal. Appl. 216 (1997), 122-163.
16. [Ito2] Ito, M.: Symmetry classification for Jackson integral associated with irreducible reduced root systems, Compositio Math. 129 (2001), 325-340.
17. [Ito3] Ito, M.: Convergence and asymptotic behavior of Jackson integrals associated with irreducible reduced root systems, Preprint, 2000.
18. 4, Ramanujan J. 6 (2002), 279-293.
19. [Ito5] Ito, M.: Askey-Wilson type integrals associated with root systems, Preprint, 2002.
20. n, Mem. Amer. Math. Soc. 108, 1994.
21. [Mi] Milne, S. C.: Basic hypergeometric series very well-poised in U(n), J. Math. Anal. Appl. 122 (1987), 223-256.
22. [Ma1] Macdonald, I. G.: Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 998-1007.
23. [Ma2] Macdonald, I. G.: A formal identity for affine root systems, Preprint, 1996.
24. [S] Schlosser, M.: Summation theorems for multidimensional basic hypergeometric series by determinant evaluations, Discrete Math. 210 (2000), 151-169.