 94128 Delius G.W., Zhang Y.Z.
 Finite dimensional representatins of quantum affine algebras
(50K, LATEX)
May 9, 94

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We give a general construction for finite dimensional representations
of $U_q(\hat{\G})$ where $\hat{\G}$ is a nontwisted affine
KacMoody 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.
 Files:
94128.tex