94-128 Delius G.W., Zhang Y.-Z.

Finite dimensional representatins of quantum affine algebras (50K, LATEX) May 9, 94

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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 $q = 1$. %This implies that affinizable representations are in general reducible ones. 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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