Topological G/G WZW model in the generalized momentum representation

We consider the topological gauged WZW model in the generalized momentum representation. The chiral field g is interpreted as a counterpart of the electric field E of conventional gauge theories. The gauge dependence of wave functionals Ψ(g) is governed by a new gauge cocycle φ_GWZW. We evaluate this cocycle explicitly using the machinery of Poisson σ models. In this approach the GWZW model is reformulated as a Schwarz-type topological theory so that the action does not depend on the world-sheet metric. The equivalence of this new formulation to the original one is proved for genus one and conjectured for an arbitary genus Riemann surface. As a by-product we discover a new way to explain the appearance of quantum groups in the WZW model.