  This note has two purposes. First we establish that the map defined in [L,
$\S 40.2.5$ (a)] is an isomorphism for certain admissible sequences. Second we
show the map gives rise to a convex basis of Poincar\'e--Birkhoff--Witt (PBW)
type for $\bup$, an affine untwisted quantized enveloping algebra of
Drinfel$'$d and Jimbo. The computations in this paper are made possible by
extending the usual braid group action by certain outer automorphisms of the
algebra.
