From Toda hierarchy to KP hierarchy

Author:

Di Yang, Jian Zhou

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph), Algebraic Geometry (math.AG)

journal:

date:

2023-11-10 16:00:00

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.

PDF: From Toda hierarchy to KP hierarchy.pdf