The genus one Complex Quantum Chern-Simons representation of the Mapping Class Group

In this paper we compute explicitly, following Witten's prescription, the quantum representation of the mapping class group in genus one for complex quantum Chern-Simons theory associated to any simple and simply connected complex gauge group $G_{\mathbb C}$. We use a generalization of the Weil-Gel'fand-Zak transform to exhibit an explicit expression for the representation.

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