  We study PBW bases of the untwisted quantum loop group $U_q(L\mathfrak{g})$
(in the Drinfeld new presentation) using the combinatorics of loop words, by
generalizing the treatment of [26,27,40] in the finite type case. As an
application, we prove that Enriquez' homomorphism [10] from the positive half
of the quantum loop group to the trigonometric degeneration of
Feigin-Odesskii's elliptic algebra [13] associated to $\mathfrak{g}$ is an
isomorphism.
