2003/07/14 by Alexander Givental, Alexander B. Givental, Givental, Alexander B. +3 · 1 citation
Mathematics · Physics and Astronomy · #14N35 #17B69 #32S30 #37K30 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.AG #math.RT #msc:14N35 #msc:17B69 #msc:32S30 #msc:37K30
paper · pdf · doi:10.48550/arxiv.math/0307176
24 pages
arxiv created 2003/07/14 · openalex publication_date 2003/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper math.AG/0108100 gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In math.AG/0209205, 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 An-1-singularity satisfies the modulo-n reduction of the KP-hierarchy. In this paper, we identify the hierarchy satisfied by the total descendent potential of a simple singularity of the A,D,E-type. Our description of the hierarchy is parallel to the vertex operator construction of Kac -- Wakimoto 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.