From Toda Hierarchy to KP Hierarchy
Exactly Solvable and Integrable Systems
2025-08-12 v3 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
Using the matrix-resolvent method and a formula of the second-named author on the -point function for a KP tau-function, we show that the tau-function of an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We then generalize this result to tau-functions for the extended Toda hierarchy (ETH) by developing the matrix-resolvent method for the ETH. As an example the partition function of Gromov-Witten invariants of the complex projective line is a KP tau-function, and an application on irreducible representations of the symmetric group is obtained.
Keywords
Cite
@article{arxiv.2311.06506,
title = {From Toda Hierarchy to KP Hierarchy},
author = {Di Yang and Jian Zhou},
journal= {arXiv preprint arXiv:2311.06506},
year = {2025}
}