A Finite Dimensional Gauge Problem in the WZNW Model

The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each of these matrix algebras admits an ideal such that the corresponding factor algebra is finite dimensional. The structure of superselection sectors of the (diagonal) 2D WZNW model is then reduced to a finite dimensional problem of a gauge theory type. For n=2 this problem is solved using a generalized BRS formalism.