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

Abstract

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.

References in corpus (6)

• Integrable Hierarchies and Dispersionless Limit
• Toda Lattice Hierarchy and Generalized String Equations
• Quantum and Classical Aspects of Deformed $c=1$ Strings.
• Fermionic representation for basic hypergeometric functions related to Schur polynomials
• Additional symmetries of KP, Grassmannian, and the string equation II
• Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies.

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