On Ordinary, Linear q-Difference Equations, with Applications to q-Sato Theory

Abstract

The purpose of this paper is to develop the theory of ordinary, linear q-difference equations, in particular the homogeneous case; we show that there are many similarities to differential equations. In the second part we study the applications to a q-analogue of Sato theory. The q-Schur polynomials act as basis function, similar to q-Appell polynomials. The Ward q-addition plays a crucial role as operation for the function argument in the matrix q-exponential and for the q-Schur polynomials.