Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

Journal of the Physical Society of Japan

Volumn 65, Issue 8, 1996, Pages 2423-2439

  Ujino, Hideaki ^a   Wadati, Miki ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Dunkl operator; Hi Jack symmetric polynomials; Quantum Calogero model; Quantum inverse scattering method (QISM); Rodrigues formula

Indexed keywords

EID: 0030505268     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.65.2423     Document Type: Article

References (29)

1. F. Calogero: J. Math. Phys. 12 (1971) 419.
2. A. P. Polychronakos: Phys. Rev. Lett. 69 (1992) 703.
3. H. Ujino and M. Wadati: Chaos, Solitons and Fractals 5 (1995) 109.
4. H. Ujino and M. Wadati: J. Phys. Soc. Jpn. 63 (1994) 3583.
5. H. Ujino and M. Wadati: J. Phys. Soc. Jpn. 64 (1995) 39.
6. H. Ujino and M. Wadati: J. Phys. Soc. Jpn. 64 (1995) 4121.
7. B. Sutherland: J. Math. Phys. 12 (1971) 246.
8. R. P. Stanley: Adv. Math. 77 (1988) 76.
9. I. G. Macdonald: Symmetric Functions and Hall Polynomials (Clarendon Press, Oxford, 1995) 2nd ed.
10. D. Bernard, M. Gaudin, F. D. M. Haldane and V. Pasquier: J. Phys. A: Math. Gen. 26 (1993) 5219.
11. D. Bernard, K. Hikami and M. Wadati: New Developments of Integrable Systems and Long-Ranged Interaction Models, ed. M. L. Ge and Y. S Wu (World Scientific, Singapore, 1995) p. 1.
12. K. Hikami and M. Wadati: J. Phys. Soc. Jpn. 62 (1993) 4203.
13. K. Hikami: J. Phys. A: Math. Gen. 28 (1995) L131.
14. H. Ujino and M. Wadati: J. Phys. Soc. Jpn. 64 (1995) 2703.
15. H. Ujino and M. Wadati: J. Phys. Soc. Jpn. 65 (1996) 653.
16. L. Lapointe and L. Vinet: Commun. Math. Phys. 178 (1996) 425.
17. L. Brink, T. H. Hansson and M. A. Vasiliev: Phys. Lett. B 286 (1992) 109.
18. L. Brink, T. H. Hansson, S. Konstein and M. A. Vasiliev: Nucl. Phys. B 401 (1993) 591.
19. L. Lapointe and L. Vinet: IMRN 9 (1995) 419.
20. P. J. Forrester: Nucl. Phys. B 388 (1992) 671.
21. P. J. Forrester: Nucl. Phys. B 416 (1994) 377.
22. F. Lesage, V. Pasquier and D. Serban: Nucl. Phys. B 435 (1995) 585.
23. Z. N. C. Ha: Nucl, Phys. B 435 (1995) 604.
24. I. G. Macdonald: Algebraic Groups, Utrecht, 1986, Proceedings, Lecture Notes in Mathematics 1271 ed. A., M. Cohen, W. H. Hesselink, W. L. J. van der Kallen and J. R. Strooker (Springer-Verlag, Berlin/Heidelberg/New York, 1987) p. 189.
25. H. Awata, Y. Matsuo, S. Odake and J. Shiraishi: Nucl. Phys. B 449 (1995) 347.
26. D. Uglov: preprint, hep-th/9601170.
27. 7) S. N. M. Ruijsenaars: Commun. Math. Phys. 110 (1987) 191.
28. J. F. van Diejen: J. Math. Phys. 36 (1995) 1299.
29. M. A. Olshanetsky and A. M. Perelomov: Phys. Rep. 94 (1983) 313.