Quantum exceptional group G₂ and its conjugacy classes

2016/09/08 by Alexander Baranov, Baranov, Alexander, Andrey Mudrov +3
Mathematics · #17B37 #81R50 #81R60 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:81R50 #msc:81R60

paper · pdf · doi:10.48550/arxiv.1609.02483

26 pages, 1 figure

arxiv created 2016/09/08 · arxiv updated 2016/09/09

Abstract

We construct quantization of semisimple conjugacy classes of the exceptional group G=G₂ along with and by means of their exact representations in highest weight modules of the quantum group U_q(\mathfrakg). With every point t of a fixed maximal torus we associate a highest weight module M_t over U_q(\mathfrakg) and realize the quantized polynomial algebra of the class of t by linear operators on M_t. Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.

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