Representation Theory of Lattice Current Algebras

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 $U_q(\sg)$. 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.

35 pages, LaTeX file, the revised version of the paper, to be published in Commun. Math. Phys. , the definition of the fusion product for lattice current algebras is corrected

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• Quantum matrix algebra for the SU(n) WZNW model
• A Finite Dimensional Gauge Problem in the WZNW Model
• On the Structure of Monodromy Algebras and Drinfeld Doubles
• Numerical characteristics of groups and their interrelations
• Yetter--Drinfeld structures on Heisenberg doubles and chains