The space of monodromy data for the Jimbo–Sakai family of q-difference equations

Abstract

We formulate a geometric Riemann-Hilbert correspondence that applies to the derivation by Jimbo and Sakai of equation $q$-PVI from ``isomonodromy'' conditions. This is a step within work in progress towards the application of $q$-isomonodromy and $q$-isoStokes to $q$-Painleve.