On G-function of Frobenius manifolds related to Hurwitz spaces
| dc.creator | Kokotov, A. | |
| dc.creator | Korotkin, D. | |
| dc.date | 2003-06-21 | |
| dc.date.accessioned | 2026-07-07T04:30:18Z | |
| dc.date.available | 2026-07-07T04:30:18Z | |
| dc.description | The semisimple Frobenius manifolds related to the Hurwitz spaces $H_{g,N}(k_1, ..., k_l)$ are considered. We show that the corresponding isomonodromic tau-function $τ_I$ coincides with $(-1/2)$-power of the Bergmann tau-function which was introduced in a recent work by the authors \cite{KokKor}. This enables us to calculate explicitly the $G$-function of Frobenius manifolds related to the Hurwitz spaces $H_{0, N}(k_1, ..., k_l)$ and $H_{1, N}(k_1, ..., k_l)$. As simple consequences we get formulas for the $G$-functions of the Frobenius manifolds ${\mathbb C}^N/\tilde{W}^k(A_{N-1})$ and ${\mathbb C}\times{\mathbb C}^{N-1}\times\{\Im z >0\}/J(A_{N-1})$, where $\tilde{W}^k(A_{N-1})$ is an extended affine Weyl group and $J(A_{N-1})$ is a Jacobi group, in particular, proving the conjecture of \cite{Strachan}. In case of Frobenius manifolds related to Hurwitz spaces $H_{g, N}(k_1, ..., k_l)$ with $g\geq2$ we obtain formulas for $|τ_I|^2$ which allows to compute the real part of the $G$-function. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0306053 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0306053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57423 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | On G-function of Frobenius manifolds related to Hurwitz spaces | |
| dc.type | text |