BIMODULE PROPERTIES OF GROUP-VALUED LOCAL-FIELDS AND QUANTUM-GROUP DIFFERENCE-EQUATIONS

We give an explicit construction of the quantum-group generators - loc al, semi-local, and global - in terms of the group-valued quantum fiel ds (g) over tilde and (g) over tilde(-1) in the Wess-Zumino-Novikov-Wi tten (WZNW) theory. The algebras among the generators and the fields m ake concrete and clear the bimodule properties of the (g) over tilde a nd the (g) over tilde(-1) fields. We show that the correlation functio ns of the (g) over tilde and (g) over tilde(-1) fields in the vacuum s tate defined through the semi-local quantum-group generator satisfy a set of quantum-group difference equations. We give the explicit soluti on for the two-point function. A similar formulation can also be done for the quantum self-dual Yang-Mills (SDYM) theory in four dimensions.