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We discuss the proof of Kazhdan and Lusztig of the equivalence of theDrinfeld category D(g,h) of g-modules and the category of finite dimensionalUq(g)-modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists theresult is formulated as the existence for each h\in iR of a normalized unitary2-cochain F on the dual \hat G of a compact simple Lie group G such that theconvolution algebra of G with the coproduct twisted by F is *-isomorphic to theconvolution algebra of the q-deformation G_q of G, while the coboundary ofF^{-1} coincides with Drinfeld's KZ-associator defined via monodromy of theKnizhnik-Zamolodchikov equations.

Notes on the Kazhdan-Lusztig theorem on equivalence of the Drinfeld category and the category of Uq(g)-modules