A $q$-analogue of the matrix sixth Painlevé system

Abstract

We derive a q-analogue of the matrix sixth Painlevé system via a connection-preserving deformation of a certain Fuchsian linear q-difference system. In specifying the linear q-difference system, we utilize the correspondence between linear differential systems and linear q-difference systems from the viewpoint of the spectral type. The system of non-linear q-difference equations thus obtained can also be regarded as a non-abelian analogue of Jimbo-Sakai's q-P VI .