# Finite Dimensional Representations of Quantum Affine Algebras

Research paper by **Gustav W. Delius, Yao-Zhong Zhang**

Indexed on: **26 Mar '94**Published on: **26 Mar '94**Published in: **High Energy Physics - Theory**

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join for free

#### Abstract

We give a general construction for finite dimensional representations of
$U_q(\hat{\G})$ where $\hat{\G}$ is a non-twisted affine Kac-Moody algebra with
no derivation and zero central charge. At $q=1$ this is trivial because
$U(\hat{\G})=U({\G})\otimes \C(x,x^{-1})$ with $\G$ a finite dimensional Lie
algebra. But this fact no longer holds after quantum deformation. In most cases
it is necessary to take the direct sum of several irreducible
$U_q({\G})$-modules to form an irreducible $U_q(\hat{\G})$-module which becomes
reducible at $q = 1$. We illustrate our technique by working out explicit
examples for $\hat{\G}=\hat{C}_2$ and $\hat{\G}=\hat{G}_2$. These finite
dimensional modules determine the multiplet structure of solitons in affine
Toda theory.