Geodesic
Discrete Series of Representations for the Modular Double of the Quantum Group $U_q(\operatorname{sl}(2,\mathbb{R}))$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 98-104.

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The modular double of the quantum group $U_q(\operatorname{sl}(2))$ with deformation parameter $q=e^{i\pi\tau}$ is a natural object explicitly taking into account the duality $\tau\mapsto 1/\tau$. The use of the modular double in conformal field theory allows one to consider the region $1$ for the central charge of the Virasoro algebra when $|\tau|=1$. In this paper, a new discrete series of representations for the modular double of $U_q(\operatorname{sl}(2,\mathbb{R}))$ is found for such $\tau$.
Keywords: representation theory, quantum group, modular double. 
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L. D. Faddeev. Discrete Series of Representations for the Modular Double of the Quantum Group $U_q(\operatorname{sl}(2,\mathbb{R}))$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 98-104. http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a7/

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