Formulas for A_n and B_n-solutions of WDVV equations

Abstract

The simplest non-trivial solutions of WDVV equations are A_n and B_n-potentials, which describe metrics of K.Saito on spaces of versal deformation of A_n and B_n-singularities. These are some polynomials, which were known for $n⩽$ 4. We find some recurrence relations, which give a possibility to find all A_n and B_n-potentials. In passing we give recurrence formulas for coefficients of dispersionless KP hierarchy.

arXiv comment12 pages, AmsTex, simplification of formulas

References in corpus (2)

• On Dubrovin Topological Field Theories
• Painleve' transcendents and two-dimensional topological field theory

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• Diagonal invariants and genus-zero Hurwitz Frobenius manifolds