Kavli Affiliate: Todor Milanov
| Summary:
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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