  We give an explicit construction of the quantum-group generators ---local,
semi-local, and global --- in terms of the group-valued quantum fields $\tilde
g$ and $\tilde g^{-1}$ in the Wess-Zumino-Novikov-Witten (WZNW) theory. The
algebras among the generators and the fields make concrete and clear the
bi-module properties of the $\tilde g$ and the $\tilde g^{-1}$ fields. We show
that the correlation functions of the $\tilde g$ and $\tilde g^{-1}$ 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.
