Givental Graphs and Inversion Symmetry |
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Authors: | Petr Dunin-Barkowski Sergey Shadrin Loek Spitz |
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Affiliation: | 1. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P. O. Box 94248, 1090 GE, Amsterdam, The Netherlands 2. ITEP, Moscow, Russia
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Abstract: | Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy. |
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