Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP^1 orbifolds

Abstract

We prove that the Hirota quadratic equations of Milanov and Tseng define an integrable hierarchy which is equivalent to the extended bigraded Toda hierarchy. In particular this proves a conjecture of Milanov-Tseng that relates the total descendent potential of the orbifold $C_{k,m}$ with a tau function of the bigraded Toda hierarchy.

17 pages

References in corpus (1)

• The Extended Bigraded Toda hierarchy

Cited by in corpus (14)

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• The extended $Z_N$-Toda hierarchy
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• Bilinear equations in Darboux transformations by Boson-Fermion correspondence
• Additional symmetries of the extended bigraded Toda hierarchy
• Higher genera Catalan numbers and Hirota equations for extended nonlinear Schroedinger hierarchy
• Orbifold melting crystal models and reductions of Toda hierarchy
• Quantum torus algebras and B(C) type Toda systems
• Multi-fold Darboux transformations of the extended bigraded Toda hierarchy
• Extended lattice Gelfand-Dickey hierarchy
• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy
• Dressing operators in equivariant Gromov-Witten theory of ${\mathbb{CP}}^1$
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy