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arXiv · 1909.12735

The extended D-Toda hierarchy

Jipeng Cheng·Todor Milanov
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Abstract

In a companion paper 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 $A$

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Jipeng Cheng, Todor Milanov. 2019-09-27. The extended D-Toda hierarchy. https://arxiv.org/abs/1909.12735

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