Ah. Bougourzi et Ra. Weston, MATRIX-ELEMENTS OF U(Q)[SU(2)(K)] VERTEX OPERATORS VIA BOSONIZATION, International journal of modern physics A, 9(25), 1994, pp. 4431-4447
We construct bosonized vertex operators (VO's) and conjugate vertex op
erators (CVO's) of U(q)[su(2)k] for arbitrary level k and representati
on j less-than-or-equal-to k/2. Both are obtained directly as two solu
tions of the defining condition of vertex operators - namely that they
intertwine U(q)[su(2)k] modules. We construct the screening charge an
d present a formula for the n-point function. Specializing to j = 1/2
we construct all VO's and CVO's explicitly. The existence of the CVO a
llows us to place the calculation of the two-point function on the sam
e footing as k = 1; that is, it is obtained without screening currents
and involves only a single integral from the CVO. This integral is ev
aluated and the resulting function is shown to obey the q-KZ equation
and to reduce simply to both the expected k = 1 and q = 1 limits.