Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation

Details Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation

2000-03-13

arxiv.org/abs/math-ph/0003011v2

Physics

Mathematical Physics

Scientific paper

10.1016/S0167-2789(01)00158-0

We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variable shifts parameters of hypergeometric functions. The role of additional symmetries in generating hypergeometric tau-functions is explained.

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