  The zero modes of the monodromy extended SU(2) WZNW model give rise to a
gauge theory with a finite dimensional state space. A generalized BRS operator
$A$ such that $A^h=0 (h=k+2=3,4,...$ being the height of the current algebra
representation) acts in a (2h-1)-dimensional indefinite metric space $H_I$ of
quantum group invariant vectors. The generalized cohomologies $Ker A^n/ Im
A^{h-n} (n=1,..., h-1)$ are 1-dimensional. Their direct sum spans the physical
subquotient of $H_I$.
