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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     author = {L. D. Faddeev},
     title = {Discrete {Series} of {Representations} for the {Modular} {Double} of the {Quantum} {Group} $U_q(\operatorname{sl}(2,\mathbb{R}))$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {98--104},
     publisher = {mathdoc},
     volume = {42},
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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/