We consider the quantum-mechanical algebra of observables generated by canonical quantization of $SL(2,R)$ Chern-Simons theory with rational charge on a space manifold with torus topology. We produce modular representations generalizing the representations associated to the $SU(2)$ WZW models and we exhibit the explicit polynomial representations of the corresponding fusion algebras. The relation to Kac-Wakimoto characters of highest weight $\widehat{sl}(2)$ representations with rational level is illustrated. Talk given at the Como Conference on ``Integrable Quantum Field Theories'', September 1992.
CITATION STYLE
Imbimbo, C. (1993). New Modular Representations and Fusion Algebras from Quantized SL(2,R) Chern-Simons Theories (pp. 303–315). https://doi.org/10.1007/978-1-4899-1516-0_20
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