Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Ablowitz, D. Kaup, A. Newell, H. Segur, Stud. Appl. Math. 53 (1974) 249–315
M. Adler, Inv. Math. 50 (1979) 219–248
O. Babelon, D. Bernard, Comm. Math. Phys. 149 (1992) 279–306
O. Babelon, D. Bernard, Int. J. Math. Phys. A8 (1993) 507–543
O. Babelon, L. Bonora, Phys. Lett. B244 (1990) 220
F.A. Bais, P. Bouwknegt, K. Schoutens and M. Surridge, Nucl. Phys. B304 (1988) 348–370
J. Balog, L. Feher, L. O'Raifeartaigh, P. Forgacs, A. Wipf, Ann. Phys. (NY) 203 (1990) 76
A. Belavin, A. Polyakov, A. Zamolodchikov, Nucl. Phys. B241 (1984) 333–380
D. Bernard, G. Felder, Comm. Math. Phys. 127 (1990) 145
J.N. Bernstein, I.M. Gelfand, S.I. Gelfand, Funct. Anal. Appl. 5 (1971) 1–8
J.N. Bernstein, I.M. Gelfand, S.I. Gelfand, in Representations of Lie groups, ed. I. Gelfand, 21–64, Wiley, New York 1975
M. Bershadsky, H. Ooguri, Comm. Math. Phys. 126 (1989) 49
A. Bilal, J.-L. Gervais, Phys. Lett. 206B (1988) 412; Nucl. Phys. B314 (1989) 646; B318 (1989) 579
R. Borcherds, Proc. Natl. Acad. Sci. USA, 83 (1986) 3068–3071
R. Bott, L.W. Tu, Differential forms in algebraic topology, Springer, New York 1982
P. Bouwknegt, in Infinite-dimensional Lie algebras and groups, ed. V. Kac, Adv. Ser. in Math. Phys. 7, 527–555, World Scientific, Singapore 1989
P. Bouwknegt, J. McCarthy, K. Pilch, Comm. Math. Phys. 131 (1990) 125–155
P. Bouwknegt, J. McCarthy, K. Pilch, Progr. Theor. Phys. Suppl. 102 (1990) 67
P. Bouwknegt, J. McCarthy, K. Pilch, in Strings and Symmetries, eds. N. Berkovits, e.a., 407–422. World Scientific, 1992
P. Bouwknegt, K. Schoutens, Phys. Reports 223 (1993) 183–276
P. Bowcock, P. Goddard, Nucl. Phys. B305 (1988) 685
P. Bowcock, G.M.T. Watts, Nucl. Phys. B379 (1992) 63–95
H.W. Braden, E. Corrigan, P.E. Dorey, R. Sasaki, Nucl. Phys. B338 (1990) 698
P. Christe, G. Mussardo, Nucl. Phys. B330 (1990) 465–487
J. de Boer, T. Tjin, Preprint THU-93/01, ITFA-02-93
C. De Concini, V. Kac, in Operator algebras, unitary representations, enveloping algebras, and invariant theory, eds. A. Connes e.a., Progress in Math. 92, 471–506, Birkhäuser 1990.
L.A. Dickey, Soliton Equations and Hamiltonian Systems, Adv. Ser. in Math. Phys. 12, World Scientific, Singapore, 1990
P. Di Francesco, C. Itzykson, J.-B. Zuber, Comm. Math. Phys. 140 (1991) 543–567
P. Di Francesco, P. Mathieu, Phys. Lett. B278 (1992) 79–84
P. Di Francesco, P. Mathieu, D. Sénéchal, Mod. Phys. Lett. A7 (1992) 701
V.G. Drinfeld, Sov. Math. Dokl. 32 (1985) 254
V.G. Drinfeld, V.V. Sokolov, Sov. Math. Dokl. 23 (1981) 457–462
V.G. Drinfeld, V.V. Sokolov, J. Sov. Math. 30 (1985) 1975–2035
V.G. Drinfeld, Algebra i Analiz (Leningrad Math. J.) 1, N2 (1989) 30–46
T. Eguchi, S.-K. Yang, Phys. Lett. 224B (1989) 373
T. Eguchi, S.-K. Yang, Phys. Lett. 235B (1989) 282
L.D. Faddeev, L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer, 1987
L.D. Faddeev, L.A. Takhtajan, in Lect. Notes in Phys. 246, 66. Springer, 1986
L.D. Faddeev, A. Volkov, Phys. Lett. 315B (1993) 311–318
V. Fateev, S. Lukyanov, Int. J. of Mod. Phys. A3 (1988) 507
V. Fateev, S. Lukyanov, Sov. J. Nucl. Phys. 49 (1989) 925
V. Fateev, S. Lukyanov, Kiev Preprints ITF-88-74R, ITF-88-75R, ITF-88-76R, 1988 (English translation: Sov. Sci. Rev. A Phys. 15 (1990) 1)
V. Fateev, A. Zamolodchikov, Nucl. Phys. B280 (1987) 644
V. Fateev, A. Zamolodchikov, in Physics and Mathematics of Strings, Memorial Volume for Vadim Knizhnik, eds. L. Brink, D. Friedan, A.M. Polyakov, 245–270, World Scientific, 1990
B. Feigin, E. Frenkel, Phys. Lett. B246 (1990) 75–81
B. Feigin, E. Frenkel, Lett. Math. Phys. 19 (1990) 307–317
B. Feigin, E. Frenkel, Comm. Math. Phys. 128 (1990) 161–189
B. Feigin, E. Frenkel, Int. J. Mod. Phys. A7, Supplement 1A (1992) 197–215
B. Feigin, E. Frenkel, Duke Math. Journal 64, IMRN 6 (1991) 75–82
B. Feigin, E. Frenkel, Phys. Lett. B276 (1992) 79–86
B. Feigin, E. Frenkel, Kac-Moody groups and integrability of soliton equations, Preprint RIMS-970, hep-th/9311171, to appear in Invent. Math.
B. Feigin, D. Fuchs, in Representations of Lie Groups and Related Topics, eds. A.M. Vershik and D.P. Zhelobenko, 465–554, Gordon and Breach, 1990
G. Felder, Nucl. Phys. B324 (1989) 548
G. Felder, C. Wieczerkowski, Comm. Math. Phys. 138 (1991) 583–605
J.M. Figueroa-O'Farrill, Nucl. Phys. B343 (1990) 450
E. Frenkel, Affine Kac-Moody algebras at the critical level and quantum Drinfeld-Sokolov reduction, Ph.D. Thesis, Harvard University, 1991
E. Frenkel, in “New Symmetry Principles in QFT”, eds. J. Fröhlich, e.a., 433–447, Plenum Press, 1992
E. Frenkel, V. Kac, A. Radul, W. Wang, W 1+∞ and W(gl N ) with central charge N, Preprint hepth/9405121, to appear in Comm. Math. Phys.
E. Frenkel, V. Kac, M. Wakimoto, Comm. Math. Phys. 147, (1992) 295–328
I. Frenkel, in Applications of Group Theory in Physics and Mathematical Physics, eds. M. Flato, P. Sally, G. Zuckerman, Lect. in Appl. Math. 21, 325–353. AMS, Providence, 1985
I. Frenkel and V. Kac, Invent. Math. 62 (1980), 23–66
I. Frenkel, J. Lepowsky, A. Meurman, Vertex Operator Algebras and the Monster, Academic Press 1988
I. Frenkel, Y.-Z. Huang, J. Lepowsky, Memoirs of the AMS, 594 (1993)
I. Frenkel, Y. Zhu, Duke Math. Journal 66 (1992) 123–168
P.G.O. Freund, T.R. Klassen, E. Melzer, Phys. Lett. B229 (1989) 243
D.B. Fuchs, Cohomology of Infinite-dimensional Lie Algebras, Plenum 1988
C.S. Gardner, J. Math. Phys. 12 (1971) 1548–1551
C.S. Gardner, J.M. Green, M.D. Kruskal, R.M. Miura, Phys. Rev. Lett. 19 (1967) 1095–1097
I.M. Gelfand, L.A. Dikii, Russ. Math. Surv. 30, N5 (1975) 77–113
I.M. Gelfand, L.A. Dikii, Funct. Anal. Appl. 10 (1976) 16–22
I.M. Gelfand, L.A. Dikii, A family of Hamiltonian structures connected with integrable non-linear differential equations, Preprint IPM AN SSSR, Moscow, 1978
J.-L. Gervais, Phys. Lett. B160 (1985) 277
J.-L. Gervais, Phys. Lett. B160 (1985) 279
J.-L. Gervais, A. Neveu, Nucl. Phys. B224 (1983) 329
P. Goddard, in Infinite-dimensional Lie algebras and groups ed. V. Kac, Adv. Ser. in Math. Phys. 7, 556–587, World Scientific, Singapore 1989.
A. Guichardet, Cohomologie des Groupes Topologiques et des Algebres de Lie, Cedic/Fernand Nathan, Paris 1980
T. Hollowood, P. Mansfield, Phys. Lett. 226B (1989) 73
M. Jimbo, Lett. Math. Phys. 10 (1985) 63
A. Joseph, G. Letzter, Rosso's form and quantized Kac-Moody algebras, Preprint, 1993
V. Kac, Adv. Math. 30 (1978) 85
V. Kac, Infinite-dimensional Lie Algebras, 3rd Edition, Cambridge University Press 1990
V. Kac, D. Kazhdan, Adv. Math. 34, 97–108 (1979)
B. Kostant, S. Sternberg, Ann. Phys. 176 (1987) 49
A. Kuniba, T. Nakanishi, J. Suzuki, Nucl. Phys. B356 (1991) 750–774
B. Kupershmidt, P. Mathieu, Phys. Lett. 227B (1989) 245
B. Kupershmidt, G. Wilson, Comm. Math. Phys. 81 (1981) 189–202
B. Kupershmidt, G. Wilson, Inv. Math. 62 (1981) 403–436
P. Lax, Lect. Appl. Math. 15 (1974) 85–96
A. LeClair, Preprint CLNS 93/1220, hep-th/9305110, May 1993
A.N. Leznov, M.V. Saveliev, Lett. Math. Phys. 3 (1979) 498–494
H. Li, Local systems of vertex operators, vertex superalgebras and modules, Preprint
G. Lusztig, Adv. Math. 70 (1988) 237
S. MacLane, Homology, Springer 1963
F. Malikov, Int. J. Mod. Phys. A7, Supplement 1B (1992) 623–643
Yu. I. Manin, J. Sov. Math. 11 (1978) 1–122
D. McLaughlin, J. Math. Phys. 16 (1975) 96
A. Mikhailov, M. Olshanetsky, V. Perelomov, Comm. Math. Phys. 79 (1981) 473–488
W. Nahm, Int. J. Mod. Phys. A6 (1991) 2837–2845
M. Niedermaier, Comm. Math. Phys. 148 (1992) 249–281
M. Niedermaier, Preprint DESY 92-105 (1992)
M. Niedermaier, in “New Symmetry Principles in QFT”, eds. J. Fröhlich, e.a., 493–503, Plenum Press, 1991
D. Olive, N. Turok, Nucl. Phys. B220 (1983) 491
D. Olive, N. Turok, Nucl. Phys. B265 (1985) 469
D. Olive, N. Turok, J. Underwood, Preprint, April 1993
A. Pressley, G. Segal, Loop Groups, Clarendon Press, Oxford 1986
N. Reshetikhin, F. Smirnov, Comm. Math. Phys. 131 (1990) 157–177
A. Rocha-Caridi, Trans. AMS 262 (1980) 335
R. Sasaki, I. Yamanaka, Adv. Stud. in Pure Math. 16, 271–296 (1988)
V. Schechtman, A. Varchenko, in ICM-90 Satellite Conference Proceedings Algebraic Geometry and Analytic Geometry, 182–191, Springer 1991
V. Schechtman, Duke Math. J., Int. Math. Res. Not. 2 (1992) 39–49; 10 (1992) 307–315
G. Segal, Int. J. Mod. Phys. A6 (1991) 2859–2869
E. Sklyanin, L. Takhtajan, L. Faddeev, Theor. Math. Phys. 40 (1980) 688
L. Takhtadjian, L. Faddeev, Teor. Mat. Fiz. 21 (1974) 680
A. Varchenko, Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Adv. Ser. in Math. Phys. 21, World Scientific 1995
A. Volkov, Phys. Lett. 167A (1992) 345
G. Wilson, Ergod. Th. and Dynam. Syst. 1 (1981) 361
V.E. Zakharov, L.D. Faddeev, Funct. Anal. Appl. 5 (1971) 280–287
A. Zamolodchikov, Al. Zamolodchikov, Ann. Phys. 120 (1979) 253–291
A. Zamolodchikov, Theor. Math. Phys. 65 (1985) 1205
A. Zamolodchikov, Adv. Stud. in Pure Math. 19, 641–674 (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag
About this chapter
Cite this chapter
Feigin, B., Frenkel, E. (1996). Integrals of motion and quantum groups. In: Francaviglia, M., Greco, S. (eds) Integrable Systems and Quantum Groups. Lecture Notes in Mathematics, vol 1620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094794
Download citation
DOI: https://doi.org/10.1007/BFb0094794
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60542-3
Online ISBN: 978-3-540-47706-8
eBook Packages: Springer Book Archive