Modules of derivations for toral arrangements

Let G be a connected semi-simple algebraic group over . Fix a maximal torus T in G with coordinate ring _T. Let Φ⁺ be the set of positive roots of G with respect to T. The pair (T, A), where A = {kerα}_α?φ⁺, is a toral arrangement. We show that if G is simply connected then the module of A-derivations D(A) is a free _T-module.