Notes on the Kazhdan-Lusztig theorem on equivalence of the Drinfeld category and the category of U_qg-Modules

摘要

We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category D(g,h) of g-modules and the category of finite dimensional U_qg-modules, q=e~(πih), for h ∈ ??*. Aiming at operator algebraists the result is formulated as the existence for each h ∈ i? of a normalized unitary 2-cochain F on the dual ? of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by F *-isomorphic to the convolution algebra of the q-deformation G _q of G, while the coboundary of F~(-1) coincides with Drinfeld's KZ-associator defined via monodromy of the Knizhnik-Zamolodchikov equations.