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

Let image be an untwisted affine Kac–Moody algebra. The quantum group image 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 image of the Poisson proalgebraic group image dual of image (a Kac–Moody group with Lie algebra image) 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.