Factorizable D-modules

Details Factorizable D-modules Factorizable D-modules

1996-11-18

arxiv.org/abs/q-alg/9611018v1

Mathematics

Quantum Algebra

amslatex, 18 pp

Scientific paper

A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite dimensional representations of a complex semisimple Lie algebra $\frak{g}$, with the Drinfeld's Knizhnik-Zamolodchikov tensor product. This description, together with the result of op.cit., gives a new, "Riemann-Hilbert" proof of the Drinfeld's theorem establishing an equivalence of the above tensor category with the category of finite dimensional $U_q\frak{g}$-modules ($q=\exp(2\pi i/kappa)$, $\kappa$ irrational).

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