Simple singularities and integrable hierarchies
By Alexander Givental, T. Milanov. 2003
63 citations recorded by the source corpus.
The paper [11] gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In [12], it is proved that the total descendent potential corresponding to K. Saito’s Frobenius structure on the parameter space of the miniversal deformation of the A n−1-singularity satisfies the modulo-n reduction of the KP-hierarchy. In this paper, we identify the hierarchy which is satisfied by the total descendent potential of a simple singularity of ADE type. Our description of the hierarchy is parallel to the vertex operator construction of Kac-Wakimoto [17] except that we give both some general integral formulas and explicit numerical values for certain coefficients which in the Kac-Wakimoto theory are studied on a case-by-case basis and remain, generally speaking, unknown.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b8b5b34387cce2dc57a022cb279d339c49553b15
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In Geometry and Topology
In Nuclear and High Energy Physics
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Citations in the corpus
- The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies (2008, methodology): “— M is the space of miniversal deformations of A, D, or E type singularity and the Kac-Wakimoto hierarchies corresponding to the Coxeter transformation in the Weyl algebra of the simple Lie algebras of A, D, or E type ([17], [19]).”