Darboux transformations and Fay identities for the extended bigraded Toda hierarchyThe first author is supported in part by Simons Foundation Grants 279074 and 584741

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 transformatio...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-01, Vol.53 (6)
Main Authors: Bakalov, Bojko, Yadavalli, Anila
Format: Article
Language:English
Subjects:
Darboux transformation
extended bigraded Toda hierarchy
Fay identities
Lax operator
tau-function
wave function
wave operator
Online Access:Get full text
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Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab604d