Universal Drinfeld-Sokolov reduction and matrices of complex size

Communications in Mathematical Physics

Volumn 175, Issue 1, 1996, Pages 113-134

  Khesin, Boris ^a   Malikov, Feodor ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030556976     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02101626     Document Type: Article

References (26)

1. Adler, M.: On a trace functional for formal pseudo differential operators and the symplectic structure of the Korteweg-de Vries type equations. Invent. Math. 50, no. 3, 219-248 (1978/79)
2. Arnold, V.I.: Mathematical methods of classical mechanics, Berlin, Heidelberg, New York: Springer, 2nd ed. 1989
3. N affine algebras I. Geometrical actions. Preprint ITEP-MO-94/1
4. Date, E., Jimbo, M., Kashiwara, M., Miwa, T.: Transformation group for soliton equations. Publ. RIMS 18 1077-1110 (1982)
5. Deligne, P., Milne, J.S.: Tannakian categories. Lecture Notes in Math., Vol. 900 (1982), pp. 102-229
6. Dickey, L.A.: Soliton equations and Hamiltonian systems. Advanced Series in Math. Physics, Vol. 12, Singapore: World Scientific, 1991
7. Drinfeld, V.G., Sokolov, V.V.: Lie algebras and equations of Korteweg-de Vries type. Current problems in mathematics (Moscow), Itogi Nauki i Tekhniki, Vol. 24, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. (1984), pp. 81-180 (Russian)
8. Enriques, B.: Complex parametrized W-algebras: The gl-case, Lett. Math. Phys. 31, 15-33 (1994)
9. Enriques, B., Khoroshkin, S., Radul, A., Rosly, A., Rubtsov, V.: Poisson-Lie aspects of classical W-algebras. Preprint, Ecole Polytechnique, 1993
10. Feigin, B.L.: Lie algebras gl(λ) and cohomology of a Lie algebra of differential operators. Russ. Math. Surv. 43 no. 2, 169-170 (1988)
11. Feigin, B.L., Frenkel, E.: Integrals of motion and quantum groups. To appear in Proc. CIME Summer School, Montecatini Terme, June 14-22 (1993), hep-th 9310022, pp. 66
12. Flashka, H.: On the Toda lattice I. Phys. Rev. B 9, 1924-1925 (1974)
13. Frenkel, I.B.: Orbital theory for affine Lie algebras. Invent. Math. 77, 301-352 (1984)
14. Gelfand, I.M., Dickey, L.A: A family of Hamiltonian structures associated with nonlinear integrable differential equations. Preprint, IPM AN SSSR, Moscow, 1978
15. Kac, V.G., Peterson, D.H.: Spin and wedge representations of infinite-dimensional Lie algebras and groups. Proc. Nat. Ad. Sci. USA 78, 3308-3312 (1981)
16. Khesin, B.A., Zakharevich, I.S.: Poisson-Lie group of pseudodifferential symbols and fractional KP-KdV hierarchies, C.R.Acad.Sci. 316, 621-626 (1993), Poisson-Lie group of pseudodifferential symbols. Commun. Math. Phys. 171, 475-530 (1995)
17. Khesin, B.A., Zakharevich, I.S.: Poisson-Lie group of pseudodifferential symbols and fractional KP-KdV hierarchies, C.R.Acad.Sci. 316, 621-626 (1993), Poisson-Lie group of pseudodifferential symbols. Commun. Math. Phys. 171, 475-530 (1995)
18. Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math. 81, 973-1032 (1959)
19. Kostant, B.: Lie group representations on polynomial rings. Am. J. Math. 86, 327-402 (1963)
20. Kravchenko, O.S., Khesin B.A.: Central extension of the algebra of pseudodifferential symbols. Funct. Anal. Appl. 25, no. 2, 83-85 (1991)
21. Kupershmidt, B.A., Wilson, G.: Modifying Lax equations and the second Hamiltonian structure. Invent. Math. 62, no. 3, 403-436 (1981)
22. Malikov, F., Feigin, B., Fuchs, D.: Singular vectors in Verma modules over Kac-Moody algebras. Funkc. Anal, i ego Pril. 20, no. 2, 25-37 (1986)
23. Marsden, J.E., Weinstein, A.: Reduction of symplectic manifolds with symmetries. Rep. Math. Phys. 5, 121-130 (1974)
24. Reiman, A., Semenov-Tian-Shansky, M.: Lie algebras and nonlinear partial differential equations. Sov. Math. Doklady 21, 630-636 (1980)
25. Weinstein, A.: Local structure of Poisson manifolds. J. Diff. Geom. 18, no. 3, 523-558 (1983)
26. Malikov, F.: Vanishing theorem for BRST cohomology, to appear