Factorizable Sheaves and Quantum Groups

1. Front Matter

   Pages I-X

   PDF

2. Introduction

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 1-4

3. Acknowledgement

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 5-5

4. Overview

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 6-49

5. Intersection cohomology of real arrangements

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 50-70

6. Configuration spaces and quantum groups

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 71-121

7. Tensor categories arising from configuration spaces

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 122-172

8. Localization on ℙ1

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 173-196

9. Modular structure on the category \(\mathcal{F}\mathcal{S}\)

   • Roman Bezrukavnikov, Michael Finkelberg, Vadim Schechtman

   Pages 197-251

10. Back Matter

    Pages 252-289

    PDF

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.

• Group representation
• Quantum Groups
• cohomology
• conformal field theory
• homology
• intersection cohomology
• moduli spaces of curves

Policies and ethics