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arXiv · hep-th/9403162

Finite Dimensional Representations of Quantum Affine Algebras

Gustav W. Delius·Yao-Zhong Zhang
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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.

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Gustav W. Delius, Yao-Zhong Zhang. 1994-03-26. Finite Dimensional Representations of Quantum Affine Algebras. https://doi.org/10.1088/0305-4470%2F28%2F7%2F014

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