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

Yousuke Ohyama, Jean-Pierre Ramis, Jacques Sauloy

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 withi…