Factorizable Sheaves and Quantum Groups

Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman (auth.)3540646191, 9783540646198

The book is devoted to the geometrical construction of the representations of Lusztig’s small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.

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Table of contents :
Introduction….Pages 1-4
Acknowledgement….Pages 5-5
Overview….Pages 6-49
Intersection cohomology of real arrangements….Pages 50-70
Configuration spaces and quantum groups….Pages 71-121
Tensor categories arising from configuration spaces….Pages 122-172
Localization on ℙ 1 ….Pages 173-196
Modular structure on the category $$mathcal{F}mathcal{S}$$ ….Pages 197-251