Generalized homologies for the zero modes of the SU(2) WZNW model

We generalize the BRS method for the (finite-dimensional) quantum gauge theory involved in the zero modes of the monodromy extended SU(2) WZNW model. The generalization consists of a nilpotent operator Q such that $Q^h=0$ ($h=k+2=2,3,...$ being the height of the current algebra representation) acting on an extended state space. The physical subquotient is identified with the direct sum $\oplusinf^{h-1}_{n=1}\ker(Q^n)/\im(Q^{h-n})$.