A PBW basis for Lusztig's form of untwisted affine quantum groups
Abstract
Let
g
be an untwisted affine Kac-Moody algebra over the field
K
, and let
U
q
(g)
be the associated quantum enveloping algebra; let
U
q
(g)
be the Lusztig's integer form of
U
q
(g)
, generated by
q
-divided powers of Chevalley generators over a suitable subring
R
of
K(q)
. We prove a Poincaré-Birkhoff-Witt like theorem for
U
q
(g)
, yielding a basis over
R
made of ordered products of
q
-divided powers of suitable quantum root vectors.