Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems

Journal of the Physical Society of Japan

Volumn 65, Issue 2, 1996, Pages 394-401

  Hikami, Kazuhiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Dunkl operator; Exclusion statistics; Hecke algebra; Integrable system; Inverse square interaction; Reflection equation; Root system; Yang Baxter equation

Indexed keywords

EID: 0030530060     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.65.394     Document Type: Article

References (41)

1. F. Calogero: J. Math. Phys. 10 (1969) 2191.
2. B. Sutherland: J. Math. Phys. 12 (1971) 246.
3. J. Moser: Adv. Math. 16 (1975) 197.
4. M. A. Olshanetski and A. M. Perelomov: Phys. Rep. 94 (1983) 313.
5. F. D. M. Haldane: in Correlation Effects in Low Dimensional Electron Systems, ed. A. Okiji and N. Kawakami (Springer, Berlin, 1994).
6. V. Pasquier: in Integrable Models and Strings, ed. A. Alekseev et al. (Springer, Berlin, 1994).
7. N. Kawakami: Prog. Theor. Phys. 91 (1994) 189.
8. G. F. Dunkl: Trails. Amer. Math. Soc. 311 (1989) 167.
9. I. Cherednik: Int. J. Mod. Phys. A7 Suppl. 1A (1992) 109.
10. F. D. M. Haldane: Phys. Rev. Lett. 60 (1988) 635.
11. B. S. Shastry: Phys. Rev. Lett. 60 (1988) 639.
12. K. Hikami: Nucl. Phys. B441 (1995) 530.
13. B. D. Simons and B. L. Altshuler: Phys. Rev. B50 (1994) 1102.
14. D. Bernard, V. Pasquier and D. Serban: Europhys. Lett. 30 (1995) 301.
15. D. Bernard, M. Gaudin, F. D. M. Haldane and V. Pasquier: J. Phys. A26 (1993) 5219.
16. K. Hikami: J. Phys. A28 (1995) L131.
17. T. Yamamoto: J. Phys. Soc. Jpn. 63 (1994) 1223.
18. V. M. Buchstaber, G. Felder and A. P. Veselov: Duke Math. J. 76 (1994) 885.
19. I. Cherednik: Commun. Math. Phys. 169 (1995) 441.
20. K. Hikami: preprint (1995).
21. R. J. Baxter: Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
22. M. Gaudin: La Fonction d'one de Bethe (Masson, Paris, 1983).
23. L. D. Faddeev: Int. J. Mod. Phys. A10 (1995) 1845.
24. I. Cherednik: Theor. Math. Phys. 61 (1984) 35.
25. E. K. Sklyanin: J. Phys. A21 (1988) 2375.
26. M. Gaudin: J. Phys. France 49 (1988) 1857.
27. Y. Shibukawa and K. Ueno: Lett. Math. Phys. 25 (1992) 239.
28. G. Felder and V. Pasquier: Lett. Math. Phys. 32 (1094) 167.
29. K. Hikami: J. Phys. Soc. Jpn. 64 (1995) 2257 [Errata; 64 (1995) 4057].
30. K. Hikami: Phys. Lett. A205 (1995) 167.
31. I. Frenkel and N. Reshetikhin: Commun. Math. Phys. 146 (1992) 1.
32. S. N. M. Ruijsenaars: Commun. Math. Phys. 110 (1987) 191.
33. V. Pasquier: q-alg/9508002 (1995).
34. F. D. M. Haldane: Phys. Rev. Lett. 67 (1991) 937.
35. I. Affleck and A. W. W. Ludwig: Nucl. Phys. B360 (1991) 641.
36. P. Fendley, F. Lesage and H. Saleur: J. Stat. Phys. 79 (1995) 799.
37. G. I. Olshanskiǐ: in Quantum Groups, ed. P. P. Kulish (Springer, Berlin, 1992).
38. D. Bernard, K. Hikami and M. Wadati: in New Developments of Integrable Systems and Long-Ranged Interaction Models, ed. M.-L. Ge and Y.-S. Wu (World Scientific, Singapore, 1995).
39. K. Hikami: J. Phys. Soc. Jpn. 64 (1995) 1047.
40. A. P. Polychronakos: Phys. Rev. Lett. 69 (1992) 703.
41. M. Noumi: RIMS Kokyuroku, to appear [in Japanese].