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19 August 2022
  » arxiv » hep-th/9410189

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Finite dimensional representations of quantum affine algebras at roots of unity
Jonathan Beck ; Victor G. Kac ;
Date 25 Oct 1994
Subject High Energy Physics - Theory; Quantum Algebra | hep-th math.QA
AbstractWe describe explicitly the canonical map $chi:$ Spec $ue(a{g}) ightarrow $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 $chi$ of Spec $ue(a{g})$ is the subgroup of principal adeles.
Source arXiv, hep-th/9410189
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