The extended D-Toda hierarchy

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 $A$

73 pages

References in corpus (2)

• Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies