Notes on the KazhdanLusztig theorem on equivalence of the Drinfeld category and the category of Uq(g)modules
Abstract
We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category D(g,h) of gmodules and the category of finite dimensional Uq(g)modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists the result is formulated as the existence for each h\in iR of a normalized unitary 2cochain F on the dual \hat G of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by F is *isomorphic to the convolution algebra of the qdeformation G_q of G, while the coboundary of F^{1} coincides with Drinfeld's KZassociator defined via monodromy of the KnizhnikZamolodchikov equations.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.4302
 Bibcode:
 2007arXiv0711.4302N
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Operator Algebras
 EPrint:
 40 pages