Finite Dimensional Representations of Quantum Affine Algebras

Details Finite Dimensional Representations of Quantum Affine Algebras Finite Dimensional Representations of Quantum Affine Algebras

1994-03-26

arxiv.org/abs/hep-th/9403162v1

J.Phys. A28 (1995) 1915-1928

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1088/0305-4470/28/7/014

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.

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