The algebra of q-pseudodifferential symbols and the q-W(n)KP algebra

Journal of Mathematical Physics

Volumn 37, Issue 12, 1996, Pages 6510-6529

  Mas, Javier ^a   Seco, Marcos ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030376211     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531745     Document Type: Article

References (53)

1. A. B. Zamolodchikov, Theor. Mat. Phys. 65, 1205 (1986); V. A. Fateev and S. L. Lykyanov, Int. J. Mod. Phys. A 3, 507 (1988).
2. A. B. Zamolodchikov, Theor. Mat. Phys. 65, 1205 (1986); V. A. Fateev and S. L. Lykyanov, Int. J. Mod. Phys. A 3, 507 (1988).
3. L. A. Dickey, Soliton equations and Hamiltonian systems, Advanced Series in Mathematical Physics (World Scientific, Singapore), Vol. 12.
4. V. G. Drinfel'd and V. V. Sokolov, J. Sov. Math. 30, 1975 (1984).
5. A. Capelli, C. Trugenberger, and G. Zemba, Nucl. Phys. B 396, 465 (1993); S. Iso, D. Karabali, and B. Sakita, Phys. Lett. B 296, 143 (1992).
6. A. Capelli, C. Trugenberger, and G. Zemba, Nucl. Phys. B 396, 465 (1993); S. Iso, D. Karabali, and B. Sakita, Phys. Lett. B 296, 143 (1992).
7. S. Nojiri, M. Kawamura, and A. Sugamoto, Mod. Phys. Lett. A 9, 1159 (1994), (hep-th/9409164).
8. M. Fukuma, H. Kawai, and R. Nakayama, Commun. Math. Phys. 143, 371 (1991); H. Itoyama and Y. Matsuo, Phys. Lett. B 262, 233 (1991).
9. M. Fukuma, H. Kawai, and R. Nakayama, Commun. Math. Phys. 143, 371 (1991); H. Itoyama and Y. Matsuo, Phys. Lett. B 262, 233 (1991).
10. E. Ramos and J. Roca, Nucl. Phys. B 452, 705 (1995).
11. J. M. Figueroa-O'Farrill and E. Ramos, Phys. Lett. B 282 357 (1992) (hep-th/9202040).
12. I. Bakas, Phys. Lett. B 228, 406 (1989); Commun. Math. Phys. 134, 487 (1990).
13. I. Bakas, Phys. Lett. B 228, 406 (1989); Commun. Math. Phys. 134, 487 (1990).
14. J. M. Figueroa-O'Farrill, E. Ramos, and S. Stanciu, Phys. Lett. B 297, 289 (1992).
15. J. Gervais and Y. Matsuo, Phys. Lett. B 282, 309 (1992) (hep-th/9110028).
16. See, for example, A. A. Kehagias, P. A. A. Meesen, and G. Zoupanos, Phys. Lett. B 346, 262 (1995), and references therein.
17. 1 + α as a discretization of the Virasoro algebra," hep-th/9411027; H-T. Sato, "q-Virasoro Operators from q-Noether Currents," hep-th/9510189.
18. 1 + α as a discretization of the Virasoro algebra," hep-th/9411027; H-T. Sato, "q-Virasoro Operators from q-Noether Currents," hep-th/9510189.
19. 1 + α as a discretization of the Virasoro algebra," hep-th/9411027; H-T. Sato, "q-Virasoro Operators from q-Noether Currents," hep-th/9510189.
20. 1 + α as a discretization of the Virasoro algebra," hep-th/9411027; H-T. Sato, "q-Virasoro Operators from q-Noether Currents," hep-th/9510189.
21. E. Frenkel and N. Reshetikhin, "Quantum affine algebras and deformations of the Virasoro and W-algebras," q-alg/ 9505025.
22. E. Frenkel, "Deformations of the KdV hierarchy and related soliton equations," q-alg/9511003.
23. B. Khesin, V. Lyubashenko, and C. Roger, "Extensions and contractions of the Lie algebra of q-pseudodifferential symbols," hep-th/9403189.
24. W. Oevel and O. Ragnisco, Physica A 161, 181 (1989).
25. J. M. Figueroa-O'Farrill, J. Mas, and E. Ramos, Commun. Math. Phys. 158, 17 (1993).
26. M. A. Semenov-Tyan-Shanskii, Funct. Anal. Appl. 17, 259 (1983); RIMS, Kyoto, Univ. 21, 1237 (1985).
27. M. A. Semenov-Tyan-Shanskii, Funct. Anal. Appl. 17, 259 (1983); RIMS, Kyoto, Univ. 21, 1237 (1985).
28. L. C. Li and S. Parmentier, Commun. Math. Phys. 125, 545 (1989).
29. K. Takasaki and T. Takebe, "Integrable hierarchies and dispersionless limit," hep-th/9405096; K. Ueno and K. Takasaki, Toda Lattice Hierarchy, Advanced Studies in Pure Mathematics, Vol. 4 (World Scientific, Singapore, 1984); Group Representations and Systems of Differential Equations (North-Holland, Amsterdam, 1984).
30. K. Takasaki and T. Takebe, "Integrable hierarchies and dispersionless limit," hep-th/9405096; K. Ueno and K. Takasaki, Toda Lattice Hierarchy, Advanced Studies in Pure Mathematics, Vol. 4 (World Scientific, Singapore, 1984); Group Representations and Systems of Differential Equations (North-Holland, Amsterdam, 1984).
31. K. Takasaki and T. Takebe, "Integrable hierarchies and dispersionless limit," hep-th/9405096; K. Ueno and K. Takasaki, Toda Lattice Hierarchy, Advanced Studies in Pure Mathematics, Vol. 4 (World Scientific, Singapore, 1984); Group Representations and Systems of Differential Equations (North-Holland, Amsterdam, 1984).
32. L. Bonora, C. P. Constantinidis, and E. Vinteler, "Toda lattice realization of integrable hierarchies," hep-th/9511172.
33. J. M. Figueroa-O'Farrill, "W-(super)algebras and (super)integrable hierarchies," unpublished notes. Bonn, 1992.
34. B. A. Khesin and I. S. Zakharevich, C. R. Acad. Sci. Sér. I 315, 621 (1993); Commun. Math. Phys. 171, 475 (1995) (hep-th/9312088).
35. B. A. Khesin and I. S. Zakharevich, C. R. Acad. Sci. Sér. I 315, 621 (1993); Commun. Math. Phys. 171, 475 (1995) (hep-th/9312088).
36. F. Martínez Morás, private communication.
37. O. S. Kravchenko and B. Khesin, Funct. Anal. Appl. 25, 83 (1991).
38. I. Bakas, B. Khesin, and E. Kiritsis, Commun. Math. Phys. 151, 233 (1993).
39. J. M. Figueroa-O'Farrill, J. Mas, and E. Ramos, Phys. Lett. B 299, 41 (1993).
40. A. O. Radul, Sov. Phys. JETP Lett. 50, 371 (1989); J. M. Figueroa-O'Farrill and E. Ramos, Lett. Math. Phys. 27, 223 (1993) (hep-th/9211036).
41. A. O. Radul, Sov. Phys. JETP Lett. 50, 371 (1989); J. M. Figueroa-O'Farrill and E. Ramos, Lett. Math. Phys. 27, 223 (1993) (hep-th/9211036).
42. B. A. Kupershmidt and G. Wilson, Invent. Math. 62, 403 (1981); F. Yu, Lett. Math. Phys. 29, 175 (1993).
43. B. A. Kupershmidt and G. Wilson, Invent. Math. 62, 403 (1981); F. Yu, Lett. Math. Phys. 29, 175 (1993).
44. J. Mas and E. Ramos, Phys. Lett. B 351, 194 (1995) (q-alg/9501009); J. M. Figueroa-O'Farrill and Sonia Stanciu, "Lie-Poisson groups and the Miura transformation" (q-alg/9501027).
45. J. Mas and E. Ramos, Phys. Lett. B 351, 194 (1995) (q-alg/9501009); J. M. Figueroa-O'Farrill and Sonia Stanciu, "Lie-Poisson groups and the Miura transformation" (q-alg/9501027).
46. B. A. Kupershmidt, Commun. Math. Phys. 99, 51 (1985).
47. W. Oevel and W. Strampp, Commun. Math. Phys. 157, 51 (1993).
48. D. Gieseker, "The Toda hierarchy and the KdV hierarchy," alg-geom/9509006.
49. H. Aratyn, L. A. Ferreira, J. F. Gomes, and A. H. Zimerman, Phys. Lett. B 316, 85 (1993) (hep-th/9307147).
50. O. Babelon, Phys. Lett. B 238, 234 (1990).
51. A. P. Polychronakos, Phys. Rev. Lett. 69, 703 (1991); L. Brink, T. H. Hansson, and M. A. Vasiliev, Phys. Lett. B 286, 109 (1992); V. Narayanan and M. Sivakumar, "On the W-algebra in the Calogero-Sutherland model using the Exchange operators," hep-th/9510239.
52. A. P. Polychronakos, Phys. Rev. Lett. 69, 703 (1991); L. Brink, T. H. Hansson, and M. A. Vasiliev, Phys. Lett. B 286, 109 (1992); V. Narayanan and M. Sivakumar, "On the W-algebra in the Calogero-Sutherland model using the Exchange operators," hep-th/9510239.
53. A. P. Polychronakos, Phys. Rev. Lett. 69, 703 (1991); L. Brink, T. H. Hansson, and M. A. Vasiliev, Phys. Lett. B 286, 109 (1992); V. Narayanan and M. Sivakumar, "On the W-algebra in the Calogero-Sutherland model using the Exchange operators," hep-th/9510239.