# Representation Theory of Lattice Current Algebras

@inproceedings{AYuAlekseev1996RepresentationTO,
title={Representation Theory of Lattice Current Algebras},
author={A.Yu.Alekseev and L.D.Faddeev and J.Frohlich and V.Schomerus},
year={1996}
}
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… Expand
3 Citations
A Finite Dimensional Gauge Problem in the WZNW Model
• Physics, Mathematics
• 1999
The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being anExpand
Integrable lambda models and Chern-Simons theories
A bstractIn this note we reveal a connection between the phase space of lambda models on S1×ℝ$${S}^1\times \mathbb{R}$$ and the phase space of double Chern-Simons theories on D×ℝ D\timesExpand
On the quantization of continuous non-ultralocal integrable systems
• Physics
• 2016
Abstract We discuss the quantization of non-ultralocal integrable models directly in the continuous case, using the example of the Alday–Arutyunov–Frolov model. We show that by treating fields asExpand