The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems

Communications in Mathematical Physics

Volumn 178, Issue 2, 1996, Pages 281-299

  Avan, J ^a   Babelon, O ^a   Billey, E ^a  

^a LPTHE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010118968     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02099449     Document Type: Article

References (45)

1. Calogero, F.: Exactly solvable one-dimensional many-body problems. Lett. Nuovo Cimento 13, 411 (1975). On a functional equation connected with integrable many-body problems. Lett. Nuovo Cimento 16, 77 (1976); Moser, J.: Three integrable Hamiltonian systems connected to isospectral deformations. Adv. Math. 16, 1 (1976)
2. Calogero, F.: Exactly solvable one-dimensional many-body problems. Lett. Nuovo Cimento 13, 411 (1975). On a functional equation connected with integrable many-body problems. Lett. Nuovo Cimento 16, 77 (1976); Moser, J.: Three integrable Hamiltonian systems connected to isospectral deformations. Adv. Math. 16, 1 (1976)
3. Calogero, F.: Exactly solvable one-dimensional many-body problems. Lett. Nuovo Cimento 13, 411 (1975). On a functional equation connected with integrable many-body problems. Lett. Nuovo Cimento 16, 77 (1976); Moser, J.: Three integrable Hamiltonian systems connected to isospectral deformations. Adv. Math. 16, 1 (1976)
4. Ruijsenaars, S.N.M.: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110, 191 (1987); van Deijen, J.F.: Families of commuting difference operators. Ph.D. Thesis, University of Amsterdam (1994)
5. Ruijsenaars, S.N.M.: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110, 191 (1987); van Deijen, J.F.: Families of commuting difference operators. Ph.D. Thesis, University of Amsterdam (1994)
6. Gibbons, J., Hermsen, T.: A generalisation of the Calogero-Moser system. Physica 11D, 337 (1984); Krichever, I.M., Babelon, O., Billey, E., Talon, M.: Spin generalization of Calogero-Moser system and the matrix KP equation. hep-th/9411160
7. Gibbons, J., Hermsen, T.: A generalisation of the Calogero-Moser system. Physica 11D, 337 (1984); Krichever, I.M., Babelon, O., Billey, E., Talon, M.: Spin generalization of Calogero-Moser system and the matrix KP equation. hep-th/9411160
8. Bernard, D., Gaudin, M., Haldane, F.D.M., Pasquier, V.: Yang-Baxter equation in spin chains with long range interactions. J. Phys. A: Math. Gen. 26, 5219 (1993), hep-th/9301084
9. Krichever, I., Zabrodin, A.: Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra. hep-th/9505039
10. Olshanetsky, M.A., Perelomov, A.M.: Classical integrable finite-dimensional systems related to Lie algebras. Phys. Rep. 71, 314 (1981); Quantum integrable systems related to Lie algebras. Phys. Rep. 94, 313 (1983)
11. Olshanetsky, M.A., Perelomov, A.M.: Classical integrable finite-dimensional systems related to Lie algebras. Phys. Rep. 71, 314 (1981); Quantum integrable systems related to Lie algebras. Phys. Rep. 94, 313 (1983)
12. Hitchin, N.: Stable bundles and integrable systems. Duke Math. J. 54, 91 (1987); Nekrasov, N.: Holomorphic bundles and many-body systems. hep-th/9503157
13. Hitchin, N.: Stable bundles and integrable systems. Duke Math. J. 54, 91 (1987); Nekrasov, N.: Holomorphic bundles and many-body systems. hep-th/9503157
14. Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser system from two-dimensional current algebra. Nucl. Phys. B436, 532 (1995), hep-th/9401021; Relativistic Calogero-Moser model as gauged WZW theory. Theor. Math. Phys. 100, 874 (1994), hep-th/9401017; Gorsky, A.; Integrable many body systems in the field theories. hep-th/9410228
15. Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser system from two-dimensional current algebra. Nucl. Phys. B436, 532 (1995), hep-th/9401021; Relativistic Calogero-Moser model as gauged WZW theory. Theor. Math. Phys. 100, 874 (1994), hep-th/9401017; Gorsky, A.; Integrable many body systems in the field theories. hep-th/9410228
16. Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser system from two-dimensional current algebra. Nucl. Phys. B436, 532 (1995), hep-th/9401021; Relativistic Calogero-Moser model as gauged WZW theory. Theor. Math. Phys. 100, 874 (1994), hep-th/9401017; Gorsky, A.; Integrable many body systems in the field theories. hep-th/9410228
17. Felder, G.: Conformal field theory and integrable systems associated to elliptic curves. hepth/9407154
18. Etingof, P.I., Kirillov, A.A.: On the affine analogs of Jack's and Macdonald's polynomials. hepth/9403168. MacDonald's polynomials and representations of quantum groups. Math. Res. Lett. 1, 279 (1994)
19. Etingof, P.I., Kirillov, A.A.: On the affine analogs of Jack's and Macdonald's polynomials. hepth/9403168. MacDonald's polynomials and representations of quantum groups. Math. Res. Lett. 1, 279 (1994)
20. Avan, J., Jevicki, A.: Classical integrability and higher symmetries of collective string field theory. Phys. Lett. B 266, 35 (1991)
21. Avan, J., Talon, M.: Classical R-matrix structure for the Calogero model. Phys. Lett. B 303, 33 (1993); Sklyanin, E.K.: Dynamical r-matrices for the elliptic Calogero-Moser model. Alg. and Anal. 6, 227 (1994), hep-th/9308060; Braden, H.W., Suzuki, T.: R-matrices for elliptic Calogero-Moser models. Lett. Math. Phys. 30, 147 (1994), hep-th/9309033
22. Avan, J., Talon, M.: Classical R-matrix structure for the Calogero model. Phys. Lett. B 303, 33 (1993); Sklyanin, E.K.: Dynamical r-matrices for the elliptic Calogero-Moser model. Alg. and Anal. 6, 227 (1994), hep-th/9308060; Braden, H.W., Suzuki, T.: R-matrices for elliptic Calogero-Moser models. Lett. Math. Phys. 30, 147 (1994), hep-th/9309033
23. Avan, J., Talon, M.: Classical R-matrix structure for the Calogero model. Phys. Lett. B 303, 33 (1993); Sklyanin, E.K.: Dynamical r-matrices for the elliptic Calogero-Moser model. Alg. and Anal. 6, 227 (1994), hep-th/9308060; Braden, H.W., Suzuki, T.: R-matrices for elliptic Calogero-Moser models. Lett. Math. Phys. 30, 147 (1994), hep-th/9309033
24. Billey, E., Avan, J., Babelon, O.: The r-matrix structure of the Euler-Calogero-Moser model. Phys. Lett. A 186, 114 (1994), hep-th/9312042; Exact Yangian symmetry in the classical Euler-Calogero-Moser model. Phys. Lett. A 188, 263 (1994), hep-th/9401117
25. Billey, E., Avan, J., Babelon, O.: The r-matrix structure of the Euler-Calogero-Moser model. Phys. Lett. A 186, 114 (1994), hep-th/9312042; Exact Yangian symmetry in the classical Euler-Calogero-Moser model. Phys. Lett. A 188, 263 (1994), hep-th/9401117
26. Babelon, O., Bernard, D.: The sine-Gordon solitons as an N-body problem. Phys. Lett. B 317, 363 (1993)
27. Avan, J., Rollet, G.: The classical r-matrix for the relativistic Ruijsenaars-Schneider system. Preprint Brown HET 1014 (1995)
28. Krichever, I.: Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles. Funct. Anal. Appl. 14, 282 (1980)
29. Babelon, O., Viallet, C.M.: Hamiltonian structures and Lax equations. Phys. Lett. B 237, 411 (1990)
30. Knizhnik, V.G., Zamolodchikov, A.B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B 247, 83 (1984); Bernard, D.: On the Wess-Zumino-Witten models on the torus. Nucl. Phys. B 303, 77 (1988). On the Wess-Zumino-Witten models on Riemann surfaces. Nucl. Phys. B 309, 145 (1988); Felder, G., Wieczerkowski, C.: Conformal field theory on elliptic curves and Knizhnik-Zamolodchikov-Bernard equation. hep-th/9411004
31. Knizhnik, V.G., Zamolodchikov, A.B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B 247, 83 (1984); Bernard, D.: On the Wess-Zumino-Witten models on the torus. Nucl. Phys. B 303, 77 (1988). On the Wess-Zumino-Witten models on Riemann surfaces. Nucl. Phys. B 309, 145 (1988); Felder, G., Wieczerkowski, C.: Conformal field theory on elliptic curves and Knizhnik-Zamolodchikov-Bernard equation. hep-th/9411004
32. Knizhnik, V.G., Zamolodchikov, A.B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B 247, 83 (1984); Bernard, D.: On the Wess-Zumino-Witten models on the torus. Nucl. Phys. B 303, 77 (1988). On the Wess-Zumino-Witten models on Riemann surfaces. Nucl. Phys. B 309, 145 (1988); Felder, G., Wieczerkowski, C.: Conformal field theory on elliptic curves and Knizhnik-Zamolodchikov-Bernard equation. hep-th/9411004
33. Knizhnik, V.G., Zamolodchikov, A.B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B 247, 83 (1984); Bernard, D.: On the Wess-Zumino-Witten models on the torus. Nucl. Phys. B 303, 77 (1988). On the Wess-Zumino-Witten models on Riemann surfaces. Nucl. Phys. B 309, 145 (1988); Felder, G., Wieczerkowski, C.: Conformal field theory on elliptic curves and Knizhnik-Zamolodchikov-Bernard equation. hep-th/9411004
34. x and its integrability. Lett. Math. Phys. 3, 489 (1979)
35. Babelon, O., Bonora, L., Toppan, F.: Exchange algebra and the Drinfeld-Sokolov theorem. Commun. Math. Phys. 140, 93 (1991); Balog, J., Dabrowski, L., Fehér, L.: Classical r-matrix and exchange algebra in WZNW and Toda theories. Phys. Lett. B 244, 227 (1990)
36. Babelon, O., Bonora, L., Toppan, F.: Exchange algebra and the Drinfeld-Sokolov theorem. Commun. Math. Phys. 140, 93 (1991); Balog, J., Dabrowski, L., Fehér, L.: Classical r-matrix and exchange algebra in WZNW and Toda theories. Phys. Lett. B 244, 227 (1990)
37. Gervais, J.L., Neveu, A.: Novel triangle relation and absence of tachyons in Liouville string field theory. Nucl. Phys. B 238, 125 (1984)
38. Bilal, A., Gervais, J.L.: Systematic construction of conformal theories with higher spin Virasoro symmetries. Nucl. Phys. B 318, 579 (1989)
39. n Toda field theories. Nucl. Phys. B 390, 205 (1993)
40. Faddeev, L.D.: Integrable models in 1 + 1 dimensional quantum field theory. Recent Advances in Field Theory and Statistical Mechanics (Les Houches Summer School 1982), ed. by Zuber, J.B. and Stora, R., Amsterdam: North Holland, 1984
41. Babelon, O.; Universal exchange algebra for Bloch waves and Liouville theory. Commun. Math. Phys. 139, 619 (1991)
42. Babelon, O.: Extended conformal algebra and the Yang-Baxter equation. Phys. Lett. B 215, 523 (1988)
43. Cremmer, E., Gervais, J.L.: The quantum group structure associated with non-linearly extended Virasoro algebras. Commun. Math. Phys. 134, 619 (1990)
44. 2. Lett. Math. Phys. 32, 259 (1994), hep-th/9403094
45. Maillet, J.M.: Lax equations and quantum groups. Phys. Lett. B 245, 480 (1990)