Non-Local Extensions of the Conformal Algebra : Matrix W-Algebras, Matrix KdV-Hierarchies and Non-Abelian Toda Theories

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1. 1. A. N. Leznov and M. V. Saveliev, Two-dimensional exactly and completely integrable dynamical systems, Comm. Math. Phys.89 (1983) 59. Zbl0536.35068MR707772
2. 2. J.-L. Gervais and M. V. Saveliev, Black holes from non-abelian Toda theories, Phys. Lett. B286 (1992) 271. MR1175139
3. 3. A. Bilal, Non-abelian Toda theory: a completely integrable model for strings on a black hole background, Nucl. Phys. B422 (1994) 258. Zbl0990.81695MR1289621
4. 4. A. Bilal and J.-L. Gervais, Systematic approach to conformai systems with extended Virasoro symmetries, Phys. Lett. B206 (1988) 412; MR944263
5. A. Bilal and J.-L. GervaisSystematic construction of $c=\infty$ conformal systems from classical Toda field theories, Nucl. Phys. B314 (1989) 646; MR984580
6. A. Bilal and J.-L. GervaisSystematic construction of conformal theories with higher-spin Virasoro symmetries, Nucl. Phys. B318 (1989) 579. MR999521
7. 5. A. Bilal, Multi-component KdV hierarchy, V-algebra and non-abelian Toda theory, Lett. Math. Phys.32 (1994) 103. Zbl0807.35123MR1296380
8. 6. I. Bakas, Higher spin fields and the Gelfand-Dikii algebras, Commun. Math. Phys.123 (1989) 627. Zbl0689.35100MR1006297
9. 7. I. M. Gel'fand and L. A. Dikii, Fractional powers of operators and hamiltonian systems, Funct. Anal. Applic.10 (1976) 259; Zbl0356.35072MR433508
10. I. M. Gel'fand and L. A. DikiiThe resolvent and hamiltonian systems, Funct. Anal. Applic.11 (1977) 93. Zbl0412.58018MR442984
11. 8. M. Adler, On a trace functional for pseudo-differential operators and the symplectic structure of the Korteweg-de Vries type equations, Invent, math.50 (1979) 219. Zbl0393.35058MR520927
12. 9. D. R. Lebedev and Yu. I. Manin, Gelfand-Dikii Hamiltonian operator and the coadjoint representation of the Volterra group, Funct. Anal. Applic.13 (1979) 268. Zbl0455.58012
13. 10. I. M. Gel'fand and L. A. Dikii, A family of Hamiltonian structures connected with integrable non-linear differential equations, Inst. Appl. Math. Acad. Sci. USSR preprint n° 136, 1978 (in Russian). 
14. 11. B. A. Kupershmidt and G. Wilson, Modifying Lax equations and the second Hamiltonian structure, Invent. Math.62 (1981) 403. Zbl0464.35024MR604836
15. 12. L. A. Dikii, A short proof of a Kupershmidt-Wilson theorem, Commun. Math. Phys.87 (1982) 127. Zbl0523.35091MR680652
16. 13. I. M. Gel'fand and L. A. Dikii, Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteveg-de Vries equations, Russ. Math. Surv.30 (1975) 77. Zbl0334.58007MR508337
17. 14. E. Olmedilla, L. Martinez Alonso and F. Guil, Infinite-dimensional Hamiltonian systems associated with matrix Schrödinger operators, Nuovo Cim.61B (1981) 49. MR619392
18. 15. F. Calogero and A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform associated with the multichannel Schrödinger problem, and properties of their solution, Lett. Nuovo Cim.15 (1976) 65; Zbl0435.35070MR426642
19. 16. A. Bilal, Non-local matrix generalizations of W-algebras, Princeton University preprint PUPT-1452 (March 1994), hep-th@xxx/9403197, Comm. Math. Phys. in press. Zbl0846.17026MR1331694
20. 17. P. Mathieu, Extended classical conformai algebras and the second Hamiltonian structure of Lax equations, Phys. Lett. B208 (1988) 101. MR952528
21. 18. P. Di Francesco, C. Itzykson and J.-B. Zuber, Classical W-algebras, Commun. Math. Phys.140 (1991) 543. Zbl0752.17026MR1130697
22. 19. A. B. Zamolodchikov, Infinite additional symmetries in two-dimensional conformai field theory, Theor. Math. Phys.65 (1985) 1205. MR829902