Virasoro and KdV
TLDR
In this paper, the structure of representations of the positive half of the Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations are investigated.Abstract:
We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the differential operators defined by the Virasoro conjecture and obtain some factorization properties of the solutions as well as a link to the multicomponent KP hierarchy.read more
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Lie subalgebras of Differential Operators in one Variable
TL;DR: In this article, the authors explicitly describe all Lie algebra homomorphisms from the set of differential operators to the Lie algebra of first order differential operators such that $L_0$ acts on $V$ as a first-order differential operator.
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Lie Subalgebras of Differential Operators in One Variable
TL;DR: In this paper, the authors explicitly describe all Lie algebra homomorphisms from a Lie algebra of differential operators to a first-order differential operator, such that the first order differential operator acts on the homomorphism.
References
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Journal ArticleDOI
Intersection theory on the moduli space of curves and the matrix Airy function
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.
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Loop groups and equations of KdV type
Graeme Segal,George Wilson +1 more
TL;DR: In this article, the authors decrit une construction qui attribue une solution de l'equation de Korteweg-de Vries a chaque point d'un certain grassmannien de dimension infinie.
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Soliton Equations as Dynamical Systems on Infinite Dimensional Grassmann Manifold
TL;DR: In this paper, the authors interpreted the time evolution of a solution as the dynamical motion of a point on a Grassmann manifold, and a generic solution corresponds to a generic point whose orbit (in the infinitely many time variables) is dense in the manifold, whereas degenerate solutions corresponding to points bound on those closed submanifolds that are stable under the time evolve describe the solutions to various specialized equations, such as KdV, Boussinesq, nonlinear Schrodinger, and sine-Gordon.
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Invariants of algebraic curves and topological expansion
Bertrand Eynard,Nicolas Orantin +1 more
TL;DR: In this article, an infinite sequence of invariants for any algebraic curve is defined, which can be used to define a formal series, which satisfies formally an Hirota equation, and thus obtain a new way of constructing a tau function attached to an algebraic graph.