Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Bojko Bakalov, Anila Yadavalli

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The extended bigraded Toda hierarchy (EBTH) is an integrable system satisfied by the Gromov-Witten total descendant potential of ℂℙ1 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.

Original languageEnglish (US)
Article number065202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number6
StatePublished - Jan 14 2020

Bibliographical note

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© 2020 IOP Publishing Ltd.

Copyright 2020 Elsevier B.V., All rights reserved.


  • Darboux transformation
  • Fay identities
  • Lax operator
  • extended bigraded Toda hierarchy
  • tau-function
  • wave function
  • wave operator


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