The R-matrix action of untwisted affine quantum groups at roots of 1

Let \hat{g} be an untwisted affine Kac–Moody algebra. The quantum group U_q(\hat{g}) is known to be a quasitriangular Hopf algebra (to be precise, a braided Hopf algebra). Here we prove that its unrestricted specializations at odd roots of 1 are braided too: in particular, specializing q at 1 we have that the function algebra F_q[Ĥ] of the Poisson proalgebraic group Ĥ dual of Ĝ - a Kac–Moody group with Lie algebra \hat{g} - is braided. This in turn implies also that the action of the universal R-matrix on the tensor products of pairs of Verma modules can be specialized at odd roots of 1.