Unitarity and Complete Reducibility of Certain Modules over Quantized Affine Lie Algebras

Abstract

Let $U_q(\hat{\mathcal{G}})$ denote the quantized affine Lie algebra and $U_q({\mathcal{G}}^{(1)})$ the quantized {\em nontwisted} affine Lie algebra. Let ${\mathcal{O}}_{\mathrm{fin}}$ 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 $U_q(\hat{\mathcal{G}})$ in the category ${\mathcal{O}}_{\mathrm{fin}}$ are completely reducible and that every integrable irreducible highest weight module over $U_q({\mathcal{G}}^{(1)})$ corresponding to $q>0$ is equivalent to a unitary module.

17 pages (minor errors corrected)

Cited by in corpus (3)

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