Donaldson-Thomas transformations of moduli spaces of G-local systems

If S admissible, combining our work with the work of Gross, Hacking, Keel and Kontsevich [35] we get a canonical basis in the space of regular functions on the cluster variety XPGLm,S, and in the Fomin-Zelevinsky upper cluster algebra with principal coefficients [23] related to the pair (SLm,S), as predicted by Duality Conjectures [15].