Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 037, 18 pages      arXiv:2110.03317      https://doi.org/10.3842/SIGMA.2022.037

Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals

Si-Qi Liu, Zhe Wang and Youjin Zhang
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China

Received October 28, 2021, in final form May 15, 2022; Published online May 18, 2022

Abstract
We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the intermediate long wave hierarchy, and the remaining flows coincide with a certain limit of the flows of the fractional Volterra hierarchy which controls the special cubic Hodge integrals.

Key words: integrable hierarchy; limit fractional Volterra hierarchy; intermediate long wave hierarchy.

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