2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153654Using 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.12 pages, LaTex, uses times.sty, eepic.sty; To be published in the Proceedings of XXI International Colloquium on Group Theoretical Methods in Physics, Symposium on Quantum Groups, Goslar 1996, edited by H.-D. Doebner and V.K. Dobrev, Heron Press (Sofia)Quantum Algebratext