Factorizable D-modules

Abstract

A braided tensor category $F{M}_{\kappa }$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $F{S}_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite dimensional representations of a complex semisimple Lie algebra $\mathfrak{g}$, 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 $U_q\mathfrak{g}$-modules ($q=\exp (2\pi i/kappa)$, $\kappa$ irrational).

amslatex, 18 pp

References in corpus (1)

• Localization of modules over small quantum groups

Cited by in corpus (3)

• Integral Presentations for the Universal R-matrix
• BGG resolutions via configuration spaces
• Twisted de Rham Complex on Line and Singular Vectors in $\widehat{{\mathfrak{sl}}_2}$ Verma Modules