Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-03-17
J.Math.Phys. 34 (1993) 6045-6059
Physics
High Energy Physics
High Energy Physics - Theory
17 pages (minor errors corrected)
Scientific paper
10.1063/1.530249
Let $U_q(\hat{\cal G})$ denote the quantized affine Lie algebra and $U_q({\cal G}^{(1)})$ the quantized {\em nontwisted} affine Lie algebra. Let ${\cal O}_{\rm fin}$ be the category defined in section 3. We show that when the deformation parameter $q$ is not a root of unit all integrable representations of $U_q(\hat{\cal G})$ in the category ${\cal O}_{\rm fin}$ are completely reducible and that every integrable irreducible highest weight module over $U_q({\cal G}^{(1)})$ corresponding to $q>0$ is equivalent to a unitary module.
Gould Mark D.
Zhang Yao-Zhong
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