2002/12/08 by Bharath Narayanan, Narayanan, Bharath
Mathematics · #17B67 #20G42 (Primary) #81R50 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B67 #msc:20G42 #msc:81R50
paper · pdf · doi:10.48550/arxiv.math/0212112
31 pages, adapted from PhD thesis, May 2002, KSU
arxiv created 2002/12/08 · arxiv updated 2009/11/30
Let C be a symmetrizable generalized Cartan Matrix, and q an indeterminate. \fg(C) is the Kac-Moody Lie algebra and U=Uq(\fg(C)) the associated quantum enveloping algebra over k=\Bbb Q(q). The quantum function algebra \Bbb Cq[G] is defined as a suitable U-bisubalgebra of the dual space \homk(U,k) which can be described using matrix elements of integrable U-modules. For \fg affine, the highest weight modules of Cq[G] are constructed and, assuming a minimality condition, their (unitarizable) irreducible quotients are shown to be in a 1-1 correspondence with the reduced elements of the Weyl group of \frak g(C). Further, these simple module are described in terms of the Cq[SL2]-modules obtained by restriction, and they satisfy a Tensor Product theorem, similar to the finite type case.