Rodrigues formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system

Nuclear Physics B

Volumn 571, Issue 3, 2000, Pages 632-648

  Nishino, Akinori ^a   Ujino, Hideaki ^b   Komori, Yasushi ^a   Wadati, Miki ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b GUNMA NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

Author keywords

Affine Hecke algebra; BCN type root system; Cherednik operator; Non symmetric Macdonald Koornwinder polynomial; Rodrigues formula

Indexed keywords

EID: 0034629597     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00761-0     Document Type: Article

References (44)

1. F. Calogero, J. Math. Phys. 12 (1971) 419.
2. B. Sutherland, Phys. Rev. A 4 (1971) 2019.
3. B. Sutherland, Phys. Rev. A 5 (1972) 1372.
4. C.F. Dunkl, Trans. Am. Math. Soc. 311 (1989) 311.
5. I. Cherednik, Inv. Math. 106 (1991) 411.
6. A.N. Kirillov, M. Noumi, to be published In: Proc. Workshop on Algebraic Methods and q-special Functions, May 13-17, 1996, CRM, Montreal, Canada.
7. A.A. Kirillov Jr., Bull. Am. Math. Soc. 34 (1997) 251.
8. I. Cherednik, Commun. Math. Phys. 169 (1995) 441.
9. Y. Komori, K. Hikami, Lett. Math. Phys. 43 (1998) 335.
10. Y. Komori, Lett. Math. Phys. 46 (1998) 147.
11. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd Edition (Clarendon Press, Oxford, 1995).
12. G.J. Heckman, E.M. Opdam, Compositio Math. 64 (1987) 329.
13. L. Lapointe, L. Vinet, IMRN 9 (1995) 419.
14. L. Lapointe, L. Vinet, Commun. Math. Phys. 178 (1996) 425.
15. H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 65 (1996) 653.
16. H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 65 (1996) 2423.
17. H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 66 (1997) 345.
18. L. Lapointe, L. Vinet, Lett. Math. Phys. 40 (1997) 269.
19. Y. Kajihara, M. Noumi, Compositio Math. (math/9803151).
20. I. Cherednik, Ann. Math. 95 (1995) 191.
21. I. Cherednik, IMRN 10 (1995) 483.
22. I. Cherednik, Selecta Math. 3 (1997) 459.
23. F. Knop, S. Sahi, Inv. Math. 128 (1997) 9.
24. T.H. Baker, P.J. Forrester, Nucl. Phys. B 492 (1997) 682.
25. T.H. Baker, P.J. Forrester, IMRN 14 (1997) 667.
26. H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 68 (1999) 391.
27. A. Nishino, H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 68 (1999) 797.
28. A. Nishino, H. Ujino, M. Wadati, J. Phys. Soc. Jpn 68 (1999) 701.
29. A. Nishino, H. Ujino, M. Wadati, Nucl. Phys. B 558 (1999) 589.
30. T.H. Koornwinder, Contemp. Math. 138 (1992) 189.
31. J.V. Stokman, T.H. Koornwinder, Canad. J. Math. 49 (1997) 373.
32. J.F. Van Diejen, Compositio Math. 95 (1995) 183.
33. J.F. Van Diejen, Inv. Math. 126 (1996) 319.
34. M. Noumi, RIMS Kokyuroku 919 (1995) 44, [in Japanese].
35. D. Bernard, V. Pasquier, D. Serban, Eur. Phys. Lett. 30 (1995) 301.
36. K. Hikami, J. Phys. Soc. Jpn. 65 (1996) 394.
37. S. Sahi, Ann. Math. 150 (1999) 267.
38. I.G. Macdonald, Inv. Math. 15 (1972) 91.
39. M.A. Olshanetsky, A.M. Perelomov, Phys. Rep. 94 (1983) 313.
40. S.N.M. Ruijsenaars, Commun. Math. Phys. 110 (1987) 191.
41. V.G. Kac, Infinite-dimensional Lie Algebra, 3rd Edition (Cambridge Univ. Press, Cambridge, 1990).
42. G. Lusztig, J. Am. Math. Soc. 2 (1989) 599.
43. A. Selberg, Norsk Mat. Tidsskr. 26 (1944) 71.
44. Y. Komori, Theta Functions Associated with the Affine Root Systems and the Elliptic Ruijsenaars Operators, Preprint (math. QA/9910003).