2003/06/21 by Alexey Kokotov, A. Kokotov, Kokotov, A. +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0306053
arxiv created 2003/06/21 · openalex publication_date 2003/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The semisimple Frobenius manifolds related to the Hurwitz spaces Hg,N(k1, ..., kl) are considered. We show that the corresponding isomonodromic tau-function τI coincides with (-1/2)-power of the Bergmann tau-function which was introduced in a recent work by the authors \citeKokKor. This enables us to calculate explicitly the G-function of Frobenius manifolds related to the Hurwitz spaces H0, N(k1, ..., kl) and H1, N(k1, ..., kl). As simple consequences we get formulas for the G-functions of the Frobenius manifolds \mathbb CN/Wk(AN-1) and \mathbb C×\mathbb CN-1×\\Im z >0\/J(AN-1), where Wk(AN-1) is an extended affine Weyl group and J(AN-1) is a Jacobi group, in particular, proving the conjecture of \citeStrachan. In case of Frobenius manifolds related to Hurwitz spaces Hg, N(k1, ..., kl) with g≥2 we obtain formulas for |τI|2 which allows to compute the real part of the G-function.