A formal Chevalley restriction theorem for Kac-Moody groups

Let G be a symmetrizable Kac-Moody group over a field of characteristic zero, let T be a split maximal torus of G. By using a completion of the algebra of strongly regular functions on G, and its restriction on T, we give a formal Chevalley restriction theorem. Specializing to the affine case, and to the field of complex numbers, we obtain a convergent Chevalley restriction theorem, by choosing the formal functions, which are convergent on the semi-groups of trace class elements G(tr) subset of G resp. T-tr subset of T.