Fermionic representation for basic hypergeometric functions
related to Schur polynomials
A. Yu. Orlov
Abstract: We shall present a set of fermionic representations for
the q-deformed hypergeometric functions related to Schur polynomials.
We shall show that multivariate hypergeometric functions are tau-functions
of the KP, TL hierarchies and their multicomponent counterparts. The
variables of the hypergeometric functions are the higher times of those
hierarchies. The discrete Toda lattice variables shifts parameters of
hypergeometric functions. The role of additional symmetries and of Miwa
change of variables with complex multiplicities will be explained.
(joint work with D.M. Scherbin)