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arXiv · 2311.06506

From Toda Hierarchy to KP Hierarchy

Di Yang·Jian Zhou
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Abstract

Using the matrix-resolvent method and a formula of the second-named author on the $n$-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.

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Di Yang, Jian Zhou. 2023-11-11. From Toda Hierarchy to KP Hierarchy. https://doi.org/10.3842/sigma.2025.068

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