Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Bojko Bakalov; Anila Yadavalli

doi:10.1088/1751-8121/ab604d

Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Bojko Bakalov, Anila Yadavalli

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Abstract

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 language	English (US)
Article number	065202
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	53
Issue number	6
DOIs	https://doi.org/10.1088/1751-8121/ab604d
State	Published - Jan 14 2020

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Publisher Copyright:
© 2020 IOP Publishing Ltd.

Keywords

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

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N2 - 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.

AB - 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.

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KW - Lax operator

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KW - wave function

KW - wave operator

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ER -

Darboux transformations and Fay identities for the extended bigraded Toda hierarchy

Abstract

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Keywords

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