Quantized coordinate rings, PBW-type bases and q-boson algebras

In [7], Kuniba, Okado and Yamada proved that the transition matrix of a PBW-type basis of the positive-half of the quantized universal enveloping algebra Uq(g) coincides with a matrix of the intertwiner between certain irreducible modules over the quantized coordinate ring Aq(g) introduced by Soibelman [13]. In the present article, we give a new proof of their result, by using representation theory of the q-boson algebra, and the Drinfeld pairing of Uq(g).