Quantum Moduli Spaces of Flat Connections

Abstract

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.

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)

References in corpus (2)

• Combinatorial quantization of the Hamiltonian Chern-Simons theory I
• Symplectic structure of the moduli space of flat connections on a Riemann surface

Cited by in corpus (1)

• Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras