Abstract
The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the Gromov–Witten total descendant potential of 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.
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