Geometric interpretation of the Poisson structure in affine Toda field theories

previous :: next

Geometric interpretation of the Poisson structure in affine Toda field theories

Benjamin Enriquez and Edward Frenkel

Source: Duke Math. J. Volume 92, Number 3 (1998), 459-495.

First Page: Show

Primary Subjects: 58F07

Secondary Subjects: 17B69

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231675
Mathematical Reviews number (MathSciNet): MR1620526
Zentralblatt MATH identifier: 01425108
Digital Object Identifier: doi:10.1215/S0012-7094-98-09214-6

back to Table of Contents

References

[1] M. Adler and P. van Moerbeke, Compatible Poisson structures and the Virasoro algebra, Comm. Pure Appl. Math. 47 (1994), no. 1, 5–37.

Mathematical Reviews (MathSciNet): MR95a:58052

Zentralblatt MATH: 0801.58014

Digital Object Identifier: doi:10.1002/cpa.3160470103

[2] A. V. Antonov, A. A. Bélov, and B. L. Feigin, Geometric description of the local integrals of motion of the Maxwell-Bloch equation, Modern Phys. Lett. A 10 (1995), 1209–1224.

[3] O. Babelon, F. Toppan, and L. Bonora, Exchange algebra and the Drinfeld-Sokolov theorem, Comm. Math. Phys. 140 (1991), no. 1, 93–117.

Mathematical Reviews (MathSciNet): MR94a:58084

Zentralblatt MATH: 0746.17016

Digital Object Identifier: doi:10.1007/BF02099292

Project Euclid: euclid.cmp/1104247909

[4] V. V. Bazhanov, S. L. Lukyanov, and A. B. Zamolodchikov, Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz, Comm. Math. Phys. 177 (1996), no. 2, 381–398, hep-th/9412229.

Mathematical Reviews (MathSciNet): MR97c:81165

Zentralblatt MATH: 0851.35113

Digital Object Identifier: doi:10.1007/BF02101898

Project Euclid: euclid.cmp/1104286333

[5] A. A. Beilinson and V. G. Drinfeld, Chiral algebras, preprint.

[6] R. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 10, 3068–3071.

Mathematical Reviews (MathSciNet): MR87m:17033

Zentralblatt MATH: 0613.17012

Digital Object Identifier: doi:10.1073/pnas.83.10.3068

JSTOR: links.jstor.org

[7] V. G. Drinfeld and V. V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, Soviet Math. Dokl. 23 (1981), 457–62 (in Russian), trans. in J. Soviet Math. 30 (1985), 1975–2035.

Zentralblatt MATH: 0513.35073

Mathematical Reviews (MathSciNet): MR760998

[8] B. Enriquez, Nilpotent action on the KdV variables and $2$-dimensional Drinfel'd-Sokolov reduction, Teoret. Mat. Fiz. 98 (1994), no. 3, 375–378, trans. in Theoret. and Math. Phys. 98 (1994), 256–258.

Mathematical Reviews (MathSciNet): MR95k:58073

Zentralblatt MATH: 0833.35123

[9] B. Enriquez and B. Feigin, Integrals of motion of classical lattice sine-Gordon system, Teoret. Mat. Fiz. 103 (1995), no. 3, 507–528, trans. in Theoret. and Math. Phys. 103 (1995) 738–756, hep-th/9409075.

Mathematical Reviews (MathSciNet): MR99e:58095

Zentralblatt MATH: 0855.35113

[10] B. Enriquez and E. Frenkel, Equivalence of two approaches to integrable hierarchies of KdV type, Comm. Math. Phys. 185 (1997), no. 1, 211–230.

Mathematical Reviews (MathSciNet): MR98i:58114

Zentralblatt MATH: 0873.35080

Digital Object Identifier: doi:10.1007/s002200050088

[11] B. Enriquez, V. Rubtsov, and A. Orlov, Higher Hamiltonian structures (the $\rm sl\sb 2$ case), Pis'ma Zh. Èksper. Teoret. Fiz. 58 (1993), no. 8, 677–683, (in Russian); trans. in JETP Lett. 58 (1993), 658–664; hep-th/9309038.

Mathematical Reviews (MathSciNet): MR95d:58068

[12] L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987.

Mathematical Reviews (MathSciNet): MR89m:58103

Zentralblatt MATH: 0632.58004

[13] B. Feigin and E. Frenkel, Integrals of motion and quantum groups, Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., vol. 1620, Springer, Berlin, 1996, hep-th/9310022, pp. 349–418.

Mathematical Reviews (MathSciNet): MR97d:58093

Zentralblatt MATH: 0885.58034

Digital Object Identifier: doi:10.1007/BFb0094794

[14] B. Feigin and E. Frenkel, Kac-Moody groups and integrability of soliton equations, Invent. Math. 120 (1995), no. 2, 379–408, hep-th/9311171.

Mathematical Reviews (MathSciNet): MR96i:58072

Zentralblatt MATH: 0829.58021

Digital Object Identifier: doi:10.1007/BF01241134

[15] B. Feigin and E. Frenkel, Nonlinear Schrödinger equations and Wakimoto modules, unpublished manuscript, 1994.

[16] M. A. I. Flohr, On fusion rules in logarithmic conformal field theories, Internat. J. Modern Phys. A 12 (1997), no. 10, 1943–1958.

Mathematical Reviews (MathSciNet): MR99b:81216

Zentralblatt MATH: 0985.81738

Digital Object Identifier: doi:10.1142/S0217751X97001225

[17] I. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster, Pure and Applied Mathematics, vol. 134, Academic Press Inc., Boston, MA, 1988.

Mathematical Reviews (MathSciNet): MR90h:17026

Zentralblatt MATH: 0674.17001

[18] I. M. Gelfand and I. Ja. Dorfman, Hamiltonian operators and algebraic structures associated with them, Funktsional. Anal. i Prilozhen. 13 (1979), no. 4, 13–30, 96 (Russian).

Mathematical Reviews (MathSciNet): MR81c:58035

[19] V. Gurarie, Logarithmic operators in conformal field theory, Nuclear Phys. B 410 (1993), no. 3, 535–549.

Mathematical Reviews (MathSciNet): MR94k:81261

Zentralblatt MATH: 0990.81686

Digital Object Identifier: doi:10.1016/0550-3213(93)90528-W

[20] V. G. Kac, Infinite-dimensional Lie algebras,3rd ed., Cambridge University Press, Cambridge, 1990.

Mathematical Reviews (MathSciNet): MR92k:17038

Zentralblatt MATH: 0716.17022

[21] D. R. Lebedev and A. O. Radul, Generalized internal long waves equations: construction, Hamiltonian structure, and conservation laws, Comm. Math. Phys. 91 (1983), no. 4, 543–555.

Mathematical Reviews (MathSciNet): MR85j:58076

Zentralblatt MATH: 0548.35099

Digital Object Identifier: doi:10.1007/BF01206021

Project Euclid: euclid.cmp/1103940670

[22] A. O. Radul, Description of Poisson brackets on a space of nonlocal functionals, Funktsional. Anal. i Prilozhen. 19 (1985), no. 2, 85–87, (in Russian); trans. in Functional. Anal. Appl. 19 (1985), 153–156.

Mathematical Reviews (MathSciNet): MR87c:58050

Zentralblatt MATH: 0585.58026

[23] V. E. Zaharov and A. B. Šabat, Integration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem. II, Funktsional. Anal. i Prilozhen. 13 (1979), no. 3, 13–22, (in Russian); trans. in Functional. Anal. Appl. 13 (1979), 166–174.

Mathematical Reviews (MathSciNet): MR82m:35137

Zentralblatt MATH: 0448.35090

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?