Dressing operators in equivariant Gromov-Witten theory of $\mathbb{CP}^1$
Abstract
Okounkov and Pandharipande proved that the equivariant Toda hierarchy governs the equivariant Gromov-Witten theory of . A technical clue of their method is a pair of dressing operators on the Fock space of 2D charged free fermion fields. We reformulate these operators as difference operators in the Lax formalism of the 2D Toda hierarchy. This leads to a new explanation to the question of why the equivariant Toda hierarchy emerges in the equivariant Gromov-Witten theory of . Moreover, the non-equivariant limit of these operators turns out to capture the integrable structure of the non-equivariant Gromov-Witten theory correctly.
Keywords
Cite
@article{arxiv.2103.10666,
title = {Dressing operators in equivariant Gromov-Witten theory of $\mathbb{CP}^1$},
author = {Kanehisa Takasaki},
journal= {arXiv preprint arXiv:2103.10666},
year = {2021}
}
Comments
latex2e using packages amsmath,amssymb,amsthm; (v2) A typo in the definition of E_k(z) on page 6 corrected; (v3) Some more explanations are added to the proof of Proposition 4 and the logarithmic flows of the non-equivariant limit