Integral representations of the Macdonald symmetric polynomials

Communications in Mathematical Physics

Volumn 179, Issue 3, 1996, Pages 647-666

  Awata, H ^a   Odake, S ^b   Shiraishi, J ^c  

^a KYOTO UNIVERSITY   (Japan)

^b SHINSHU UNIVERSITY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030240468     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02100101     Document Type: Article

References (51)

1. Calogero, F.: J. Math. Phys. 10, 2197-2200 (1969) Sutherland, B.: J. Math. Phys. 12, 246-250, 251-256 (1970)
2. Calogero, F.: J. Math. Phys. 10, 2197-2200 (1969) Sutherland, B.: J. Math. Phys. 12, 246-250, 251-256 (1970)
3. Haldane, F.D.M.: Phys. Rev. Lett. 60, 635-638 (1988) Shastry, B.S.: Phys. Rev. Lett. 60, 639-642 (1988)
4. Haldane, F.D.M.: Phys. Rev. Lett. 60, 635-638 (1988) Shastry, B.S.: Phys. Rev. Lett. 60, 639-642 (1988)
5. Kawakami, N.: Phys. Rev. B46, 1005-1014, 3191-3194 (1992) Ha, Z.N.C., Haldane, F.D.M.: Bull. Am. Phys. Soc. 37, 646 (1992); Phys. Rev. B46, 9359-9368 (1992)
6. Kawakami, N.: Phys. Rev. B46, 1005-1014, 3191-3194 (1992) Ha, Z.N.C., Haldane, F.D.M.: Bull. Am. Phys. Soc. 37, 646 (1992); Phys. Rev. B46, 9359-9368 (1992)
7. Kawakami, N.: Phys. Rev. B46, 1005-1014, 3191-3194 (1992) Ha, Z.N.C., Haldane, F.D.M.: Bull. Am. Phys. Soc. 37, 646 (1992); Phys. Rev. B46, 9359-9368 (1992)
8. Haldane, F.D.M.: In: Proceedings of the 16th Taniguchi Symposium. Okiji, A., Kawakami, N. eds. Berlin, Heidelberg, New York: Springer 1994
9. Iso, S., Rey, S.-J.: Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model. Preprint, UT-682, SNUTP 94-55, hep-th/9406192; as for generality, see B. I. Halperin, Developments in the Theory of the Quantum Hall Effect. cond-mat/9409036
10. Iso, S., Rey, S.-J.: Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model. Preprint, UT-682, SNUTP 94-55, hep-th/9406192; as for generality, see B. I. Halperin, Developments in the Theory of the Quantum Hall Effect. cond-mat/9409036
11. Gorsky, A., Nekrasov, N.: Nucl. Phys. B414, 213-238 (1994)
12. Minahan, J.A., Polychronakos, A.P.: Phys. Lett. B326, 288-294 (1994)
13. Avan, J., Jevicki, A.: Phys. Lett. B266, 35-41 (1991); Commun. Math. Phys. 150, 149-166 (1992)
14. Avan, J., Jevicki, A.: Phys. Lett. B266, 35-41 (1991); Commun. Math. Phys. 150, 149-166 (1992)
15. Simons, B.D., Lee, P.A., Altshuler, B.L.: Nucl. Phys. B409[FS], 487-508 (1993)
16. Haldane, F.D.M., Ha, Z.N.C., Talstra, J.C., Bernard, D., Pasquier, V.: Phys. Rev. Lett. 69, 2021-2025 (1992)
17. Bernard, D., Gaudin, M., Haldane, F.D.M., Pasquier, V.: J. Phys. A26, 5219-5236 (1993)
18. Ujino, H., Wadati, M., Hikami, K.: J. Phys. Soc. Jpn. 62, 3035-3043 (1993) Hikami, K., Wadati, M.: J. Phys. Soc. Jpn. 62, 4203-4217 (1993) Bernard, D., Hikami, K., Wadati, M.: The Yangian Deformation of the W-Algebras and the Calogero-Sutherland System. Preprint, hep-th/9412194
19. Ujino, H., Wadati, M., Hikami, K.: J. Phys. Soc. Jpn. 62, 3035-3043 (1993) Hikami, K., Wadati, M.: J. Phys. Soc. Jpn. 62, 4203-4217 (1993) Bernard, D., Hikami, K., Wadati, M.: The Yangian Deformation of the W-Algebras and the Calogero-Sutherland System. Preprint, hep-th/9412194
20. Ujino, H., Wadati, M., Hikami, K.: J. Phys. Soc. Jpn. 62, 3035-3043 (1993) Hikami, K., Wadati, M.: J. Phys. Soc. Jpn. 62, 4203-4217 (1993) Bernard, D., Hikami, K., Wadati, M.: The Yangian Deformation of the W-Algebras and the Calogero-Sutherland System. Preprint, hep-th/9412194
21. Heckman, G.J., Opdam, E.M.: Compos. Math. 64, 329-352 (1987) Heckman, G.J.: Compos. Math. 64, 353-373 (1987)
22. Heckman, G.J., Opdam, E.M.: Compos. Math. 64, 329-352 (1987) Heckman, G.J.: Compos. Math. 64, 353-373 (1987)
23. Cherednik, I.: Integration of quantum many-body problems by affine Knizhnik-Zamolodchikov equations. Preprint, RISM-776 (1991) Matsuo, A.: Invent. Math. 110, 95-121 (1992)
24. Cherednik, I.: Integration of quantum many-body problems by affine Knizhnik-Zamolodchikov equations. Preprint, RISM-776 (1991) Matsuo, A.: Invent. Math. 110, 95-121 (1992)
25. Forrester, P.J.: Nucl. Phys. B388, 671-699 (1992); B416, 377-385 (1994); J. Stat. Phys. 72, 39-50 (1993); Integration Formulas and Exact Calculations in the Calogero-Sutherland Model. Preprint, cond-mat/9408042
26. Forrester, P.J.: Nucl. Phys. B388, 671-699 (1992); B416, 377-385 (1994); J. Stat. Phys. 72, 39-50 (1993); Integration Formulas and Exact Calculations in the Calogero-Sutherland Model. Preprint, cond-mat/9408042
27. Forrester, P.J.: Nucl. Phys. B388, 671-699 (1992); B416, 377-385 (1994); J. Stat. Phys. 72, 39-50 (1993); Integration Formulas and Exact Calculations in the Calogero-Sutherland Model. Preprint, cond-mat/9408042
28. Forrester, P.J.: Nucl. Phys. B388, 671-699 (1992); B416, 377-385 (1994); J. Stat. Phys. 72, 39-50 (1993); Integration Formulas and Exact Calculations in the Calogero-Sutherland Model. Preprint, cond-mat/9408042
29. Ha, Z.N.C.: Phys. Rev. Lett. 73, 1574-1577 (1994); Nucl. Phys. B435[FS]. 604-636 (1995)
30. Ha, Z.N.C.: Phys. Rev. Lett. 73, 1574-1577 (1994); Nucl. Phys. B435[FS]. 604-636 (1995)
31. Lesage, F., Pasquier, V., Serban, D.: Nucl. Phys. B435[FS], 585-603 (1995)
32. Minahan, J.A., Polychronakos, A.P.: Phys. Rev. B50, 4236-4239 (1994)
33. Macdonald, I.G.: Symmetric Functions and Hall Polynomials (2nd ed.). Oxford: Oxford University Press, 1995; Lect. Notes in Math. 1271, 189-200 (1987), Springer; Publ. I.R.M.A. 131-171 (1988)
34. Macdonald, I.G.: Symmetric Functions and Hall Polynomials (2nd ed.). Oxford: Oxford University Press, 1995; Lect. Notes in Math. 1271, 189-200 (1987), Springer; Publ. I.R.M.A. 131-171 (1988)
35. Macdonald, I.G.: Symmetric Functions and Hall Polynomials (2nd ed.). Oxford: Oxford University Press, 1995; Lect. Notes in Math. 1271, 189-200 (1987), Springer; Publ. I.R.M.A. 131-171 (1988)
36. Stanley, R.: Adv. Math. 77, 76-115 (1989)
37. Awata, H., Matsuo, Y., Odake, S., Shiraishi, J.: Phys. Lett. B347, 49-55 (1995)
38. Mimachi, K., Yamada, Y.: Talk at the workshop "Hypergeometric Functions" at RIMS, 1994 Dec. 12-15
39. Mimachi, K., Yamada, Y.: Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials. Preprint (November 1994)
40. n Singular Vectors and Generalized Matrix Models. To appear in Soryushiron Kenkyu (Kyoto)
41. n Singular Vectors and Generalized Matrix Models. To appear in Soryushiron Kenkyu (Kyoto)
42. Ruijsenaars, S.N.M.: Commun. Math. Phys. 110, 191-213 (1987)
43. Date, E., Kashiwara, M., Jimbo, M., Miwa, T.: In: Proceedings of RIMS Symposium on Nonlinear Integral Systems, Kyoto, 1981. Jimbo, M., Miwa, T. (eds.) Singapore: World Scientific, 1983, pp. 39-119. See also Appendix B of Awata, H., Fukuma, M., Matsuo, Y., Odake, S.: Prog. Theor. Phys. Suppl. 118, (1995)
44. Date, E., Kashiwara, M., Jimbo, M., Miwa, T.: In: Proceedings of RIMS Symposium on Nonlinear Integral Systems, Kyoto, 1981. Jimbo, M., Miwa, T. (eds.) Singapore: World Scientific, 1983, pp. 39-119. See also Appendix B of Awata, H., Fukuma, M., Matsuo, Y., Odake, S.: Prog. Theor. Phys. Suppl. 118, (1995)
45. Jing, N.: Adv. Math. 87, 226-248 (1991)
46. Clavelli, L., Shapiro, J.A.: Nucl. Phys. B57, 490-535 (1973) (see Appendix C.1)
47. Frenkel, E., Reshetikhin, N.: Quantum Affine Algebras and Deformations of the Virasoro and W-Algebras. q-alg/9505025
48. 2). Preprint RIMS-910 (1992)
49. 2). Preprint RIMS-910 (1992)
50. 2). Preprint RIMS-910 (1992)
51. 2). Preprint RIMS-910 (1992)