New Modular Representations and Fusion Algebras from Quantized SL(2,R) Chern-Simons Theories

Abstract

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 $\widehat{sl}\left( 2 \right)$(2) representations with rational level is illustrated.