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Fundamental representations of quantum groups at roots of 1
Authors:Vyjayanthi Chari  Andrew Pressley
Institution:(1) Department of Mathematics, University of California, 92521 Riverside, CA, U.S.A.;(2) Department of Mathematics, King's College, Strand, WC2R 2LS London, England, U.K.
Abstract:To every finite-dimensional irreducible representation V of the quantum group Uepsi(g) where epsi is a primitive lth root of unity (l odd) and g is a finite-dimensional complex simple Lie algebra, de Concini, Kac and Procesi have associated a conjugacy class C V in the adjoint group G of g. We describe explicitly, when g is of type A n , B n , C n , or D n , the representations associated to the conjugacy classes of minimal positive dimension. We call such representations fundamental and prove that, for any conjugacy class, there is an associated representation which is contained in a tensor product of fundamental representations.
Keywords:17B37  81R50
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