Letters in Mathematical Physics

, Volume 103, Issue 5, pp 533–557 | Cite as

Givental Graphs and Inversion Symmetry

  • Petr Dunin-Barkowski
  • Sergey Shadrin
  • Loek Spitz


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.

Mathematics Subject Classification (2010)

53D45 37K10 


Frobenius manifolds Givental group action inversion transformation Feynman graphs principal hierachies 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Petr Dunin-Barkowski
    • 1
    • 2
  • Sergey Shadrin
    • 1
  • Loek Spitz
    • 1
  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.ITEPMoscowRussia

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