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Hidden quantum groups inside Kac-Moody algebra

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Abstract

A lattice analogue of the Kac-Moody algebra is constructed. It is shown that the generators of the quantum algebra with the deformation parameterq=exp(iπ/k+h) can be constructed in terms of generators of the lattice Kac-Moody algebra (LKM) with the central chargek. It appears that there exists a natural correspondence between representations of the LKM algebra and the finite dimensional quantum group. The tensor product for representations of the LKM algebra and the finite dimensional quantum algebra is suggested.

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Authors and Affiliations

  1. St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, 191011, St. Petersburg, Russia

    A. Alekseev, L. Faddeev & M. Semenov-Tian-Shansky

Authors
  1. A. Alekseev
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  2. L. Faddeev
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  3. M. Semenov-Tian-Shansky
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Communicated by N. Yu. Reshetikhin

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Alekseev, A., Faddeev, L. & Semenov-Tian-Shansky, M. Hidden quantum groups inside Kac-Moody algebra. Commun.Math. Phys. 149, 335–345 (1992). https://doi.org/10.1007/BF02097628

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  • DOI: https://doi.org/10.1007/BF02097628

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