In a companion paper (arXiv:1910.03150) to this one, we proved that the Gromov–Witten theory of a Fano orbifold line of type D is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest the name extended D-Toda hierarchy for this new system of Lax equations, because it should be viewed as the analogue of Carlet’s extended bi-graded Toda hierarchy, which is known to govern the Gromov–Witten theory of Fano orbifold lines of type A.

中文翻译：

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扩展的D-Toda层次结构

在与此相关的另一篇论文中（arXiv：1910.03150），我们证明了D型Fano单向线的Gromov-Witten理论是由Hirota双线性方程组控制的。本文的目的是证明Hirota双线性方程组的每个解决方案都可以确定Lax方程新的可积分层次的解决方案。我们建议为这个新的Lax方程组使用扩展的D-Toda层次结构名称，因为它应该被视为Carlet扩展的双级Toda层次结构的类似物，该层次结构可以控制Fano型双歧线的Gromov–Witten理论一。