# Quantum Moduli Spaces of Flat Connections

December 31, 1996

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.

open access link

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)

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