Journal ArticleDOI
Lie algebras and equations of Korteweg-de Vries type
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A survey of the theory of Kats-Moody algebras is given in this paper, which contains a description of the connection between the infinite-dimensional Lie algebra of Kats and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the inverse scattering problem.Abstract:
The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the method of the inverse scattering problem. A survey of the theory of Kats-Moody algebras is also given.read more
Citations
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Book ChapterDOI
Geometry of 2D topological field theories
TL;DR: In this paper, the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories is studied, where WDVV equations and Frobenius manifolds are discussed.
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2D gravity and random matrices
TL;DR: In this article, the authors review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices and discuss the saddle point approximation for these models, including a class of related O(n) matrix models.
Journal ArticleDOI
Moduli spaces of local systems and higher Teichmüller theory
V. V. Fock,Alexander Goncharov +1 more
TL;DR: The moduli space of positive representations is a topologically trivial open domain in the space of all representations as discussed by the authors, and all positive representations of the fundamental group of S to G(R) are faithful, discrete and positive hyperbolic.
Journal ArticleDOI
Topological strings in d < 1
TL;DR: In this article, the correlation functions in minimal topological field theories were calculated using the Landau-Ginzburg superpotential and the KdV differential operator, and it was shown that the minimal topology models are in perfect agreement with the matrix models as solved in terms of the kdV hierarchy.
Journal ArticleDOI
W symmetry in conformal field theory
TL;DR: In this article, the authors review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory and pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Journal ArticleDOI
A Simple model of the integrable Hamiltonian equation
TL;DR: In this paper, a method of analysis of the infinite-dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested, based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equation with their symmetries by using symplectic operators.
Journal ArticleDOI
Basic representations of affine Lie algebras and dual resonance models
Igor Frenkel,Victor G. Kac +1 more
Journal ArticleDOI
Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
Journal ArticleDOI
On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations
TL;DR: In this article, the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations was studied and the authors showed that it is the same as the Lie geometry behind the Lie structure of a Hamiltonian lattice.
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