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

Let (g) over cap be an untwisted affine Kac-Moody algebra. The quantum grou p U-q((g) over cap) is known to be a quasitriangular Hopf algebra (to be pr ecise, a braided Hopf algebra). Here we prove that its unrestricted special izations at odd roots of 1 are braided too: in particular, specializing q a t 1 we have that the function algebra F[(H) over cap] of the Poisson proalg ebraic group (H) over cap dual of (G) over cap (a Kac-Moody group with Lie algebra (g) over cap) 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 I. (C) 2001 Elsevier Science B.V. All r ights reserved. MSG: 17B37; 81R50.