# 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 an… Expand

Integrable lambda models and Chern-Simons theories

- Physics, Mathematics
- 2017

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\times… Expand

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 as… Expand