Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux transformations and Fay identities for the extended bigraded
  Toda hierarchy   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.

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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th