  Using the formalism of discrete quantum group gauge theory, one can construct
the quantum algebras of observables for the Hamiltonian Chern-Simons model. The
resulting moduli algebras provide quantizations of the algebra of functions on
the moduli spaces of flat connections on a punctured 2-dimensional surface. In
this note we describe some features of these moduli algebras with special
emphasis on the natural action of mapping class groups. This leads, in
particular, to a closed formula for representations of the mapping class groups
on conformal blocks.
