广义双分次Toda族的达布变换和Fay恒等式
Darboux transformations and Fay identities for the extended bigraded Toda hierarchy
摘要：
扩展的双阶Toda族（EBTH）是一个由$\mathbb{CP}^1$的Gromov-Witten全后裔势满足的具有两个轨道点的可积系统.本文给出了EBTH的τ函数的双线性方程，并由此导出了Fay恒等式，证明了达布变换对τ函数的作用是由顶点算子给出的.因此，我们得到了广义Fay恒等式.
英文摘要：
The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the Gromov-Witten total descendant potential of $\mathbb{CP}^1$ with two orbifold points. We write a bilinear equation for the tau-function of the EBTH and derive Fay identities from it. We show that the action of Darboux transformations on the tau-function is given by vertex operators. As a consequence, we obtain generalized Fay identities.
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