Quantum Moduli Spaces of Flat Connections

Details Quantum Moduli Spaces of Flat Connections Quantum Moduli Spaces of Flat Connections

1996-12-31

arxiv.org/abs/q-alg/9612037v1

Mathematics

Quantum Algebra

12 pages, LaTex, uses times.sty, eepic.sty; To be published in the Proceedings of XXI International Colloquium on Group Theore

Scientific paper

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.

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