Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Abstract

The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the Gromov-Witten total descendant potential of ${\mathbb{CP}}^1$ with two orbifold points. We write a bilinear equation for the tau-function of the EBTH and derive Fay identities from it. We show that the action of Darboux transformations on the tau-function is given by vertex operators. As a consequence, we obtain generalized Fay identities.

25 pages

References in corpus (11)

• The Extended Bigraded Toda hierarchy
• The equivariant Gromov-Witten theory of P^1
• Classification of Multidimensional Darboux Transformations: First Order and Continued Type
• Differential operators on the superline, Berezinians, and Darboux transformations
• Additional symmetries of the extended bigraded Toda hierarchy
• Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit
• Gromov--Witten Theory of CP^1 and Integrable Hierarchies
• Twisted logarithmic modules of lattice vertex algebras
• Multi-fold Darboux transformations of the extended bigraded Toda hierarchy
• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy

Cited by in corpus (1)

• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy