Finite dimensional representations of quantum affine algebras at roots of unity

Jonathan Beck; Victor G. Kac

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arXiv · hep-th/9410189

Finite dimensional representations of quantum affine algebras at roots of unity

Jonathan Beck·Victor G. Kac

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Abstract

We describe explicitly the canonical map $χ:$ Spec $\ue(\a{g})\ \rightarrow \ $Spec $\ze$, where $\ue(\a{g})$ is a quantum loop algebra at an odd root of unity $\ve$. Here $\ze$ is the center of $\ue(\a{g})$ and Spec $R$ stands for the set of all finite--dimensional irreducible representations of an algebra $R$. We show that Spec $\ze$ is a Poisson proalgebraic group which is essentially the group of points of $G$ over the regular adeles concentrated at $0$ and $\infty$. Our main result is that the image under $χ$ of Spec $\ue(\a{g})$ is the subgroup of principal adeles.

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Jonathan Beck, Victor G. Kac. 1994-11-11. Finite dimensional representations of quantum affine algebras at roots of unity. https://arxiv.org/abs/hep-th/9410189

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