Modular Double of the Quantum Group \(SL_{q}(2, \mathbb{R})\)

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)


The term “quantum group”, introduced by V. Drinfeld (Proceedings of ICM-86, Berkeley, vol. 1, p. 798. AMS, Providence, 1987), applies in fact to two dual objects: q-deformation of the algebra \(\mathcal{A}\) of functions on the Lie group and that for the universal enveloping algebra \(\mathcal{U}\) of the corresponding Lie algebra. See Faddeev [1] for the short history. It is instructive to stress, that the construction of q-deformation originates in the theory of the quantum integrable models and conformal field theory [see Faddeev [2]]. In this lecture I plan to survey some new developments on a representative example of the rang 1 SL(2) case.


Hopf Algebra Quantum Group Real Structure Spectral Problem Conformal Block 



This work was partially supported by RFBR grants 11-01-00570a and 11-01-12037ofi-m and the programm “Mathematical problems of nonlinear dynamics” of Russian Academy of Sciences.


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© Springer Japan 2014

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute, St. PetersburgRussia St. Petersburg State UniversitySt. PetersburgRussia

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