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Representation Theory of Lattice Current Algebras

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Abstract:

Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry . Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Uppsala University, Box 803 S-75108, Uppsala, Sweden.¶E-mail: alekseev@rhea.teorfys.uu.se, , , , , , SE

    Anton Y. Alekseev

  2. Institut für Theoretische Physik, ETH -- Hönggerberg, CH-8093 Zürich, Switzerland , , , , , , CH

    Jürg Fröhlich

  3. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191011, Russia. E-mail: faddeev@pdmi.ras.ru, , , , , , RU

    Ludwig D. Faddeev

  4. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany. E-mail: vschomer@x4u2.desy.de, , , , , , DE

    Volker Schomerus

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  1. Anton Y. Alekseev
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  2. Ludwig D. Faddeev
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  3. Jürg Fröhlich
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  4. Volker Schomerus
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Received: 25 April 1996 / Accepted: 14 April 1997

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Alekseev, A., Faddeev, L., Fröhlich, J. et al. Representation Theory of Lattice Current Algebras . Comm Math Phys 191, 31–60 (1998). https://doi.org/10.1007/s002200050260

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  • DOI: https://doi.org/10.1007/s002200050260

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