  Recently we suggested a new quantum algebra, the moduli algebra, which was
conjectured to be a quantum algebra of observables of the Hamiltonian Chern
Simons theory. This algebra provides the quantization of the algebra of
functions on the moduli space of flat connections on a 2-dimensional surface.
In this paper we classify unitary representations of this new algebra and
identify the corresponding representation spaces with the spaces of conformal
blocks of the WZW model. The mapping class group of the surface is proved to
act on the moduli algebra by inner automorphisms. The generators of these
automorphisms are unitary elements of the moduli algebra. They are constructed
explicitly and proved to satisfy the relations of the (unique) central
extension of the mapping class group.
