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Representation Theory of Lattice Current Algebras |
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| Authors: | Anton Y Alekseev Ludwig D Faddeev Jürg Fröhlich Volker Schomerus |
| Institution: | Institute of Theoretical Physics, Uppsala University, Box 803 S-75108, Uppsala, Sweden.?E-mail: alekseev@rhea.teorfys.uu.se, SE Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191011, Russia. E-mail: faddeev@pdmi.ras.ru, RU Institut für Theoretische Physik, ETH -- H?nggerberg, CH-8093 Zürich, Switzerland, CH II. Institut für Theoretische Physik, Universit?t Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany. E-mail: vschomer@x4u2.desy.de, DE |
| 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. Received: 25 April 1996 / Accepted: 14 April 1997 |
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