Abstract
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.
This material is based on work supported by National Science Foundation grants DMS-0072658 and DMS-0306316.
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To Alan Weinstein on his 60th birthday.
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Givental, A.B., Milanov, T.E. (2005). Simple singularities and integrable hierarchies. In: Marsden, J.E., Ratiu, T.S. (eds) The Breadth of Symplectic and Poisson Geometry. Progress in Mathematics, vol 232. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4419-9_7
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DOI: https://doi.org/10.1007/0-8176-4419-9_7
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