Representations of quantum conjugacy classes of orthosymplectic groups

2015/02/09 by Thomas Ashton, Ashton, Thomas, Andrey Mudrov +1 · 1 citation
Mathematics · #17B37 #81R50 #81R60 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:81R50 #msc:81R60

paper · pdf · doi:10.48550/arxiv.1502.02392

19 pages, no figures

arxiv created 2015/02/09 · arxiv updated 2015/02/10

Abstract

Let G be the complex symplectic or special orthogonal group and \g its Lie algebra. With every point x of the maximal torus T⊂ G we associate a highest weight module M_x over the Drinfeld-Jimbo quantum group U_q(\g) and a quantization of the conjugacy class of x by operators in \End(M_x). These quantizations are isomorphic for x lying on the same orbit of the Weyl group, and M_x support different representations of the same quantum conjugacy class.

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