Bimodule properties of group-valued local fields and quantum-group difference equations

We give an explicit construction of the quantum-group generators — local, semi-local, and global — in terms of the group-valued quantum fields g and g−1 in the Wess-Zumino-Novikov-Witten (WZNW) theory. The algebras among the generators and the fields make concrete and clear the bimodule properties of the g and the g−1 fields. We show that the correlation functions of the g and g−1 fields in the vacuum state defined through the semi-local quantum-group generator satisfy a set of quantum-group difference equations. We give the explicit solution for the two-point function. A similar formulation can also be done for the quantum self-dual Yang-Mills (SDYM) theory in four dimensions.