Representation Theory of Lattice Current Algebras

Details Representation Theory of Lattice Current Algebras Representation Theory of Lattice Current Algebras

1996-04-27

arxiv.org/abs/q-alg/9604017v2

Commun.Math.Phys. 191 (1998) 31-60

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, LaTeX file, the revised version of the paper, to be published in Commun. Math. Phys. , the definition of the fusion

Scientific paper

10.1007/s002200050260

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.

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