A PBW basis for Lusztig's form of untwisted affine quantum groups

Let (g) over cap be an untwisted affine Kac-Moody algebra over the held C, and let U-q((g) over cap) be the associated quantum enveloping algebra; let U-q((g) over cap) be the Lusztig's integer form of U-q((g) over cap), gene rated by q-divided powers of Chevalley generators over a suitable subring R of C(q). We prove a Poincare-Birkhoff-Witt like theorem for U-q((g) over c ap), yielding a basis over R made of ordered products of q-divided powers o f suitable quantum root vectors.