Coherent sheaves and categorical sl(2) actions

Abstract

We introduce the concept of a geometric categorical sl(2) action and relate it to that of a strong categorical sl(2) action. The latter is a special kind of 2-representation in the sense of Rouquier. The main result is that a geometric categorical sl(2) action induces a strong categorical sl(2) action. This allows one to apply the theory of strong sl(2) actions to various geometric situations. Our main example is the construction of a geometric categorical sl(2) action on the derived category of coherent sheaves on cotangent bundles of Grassmannians.

29 pages

References in corpus (3)

• A diagrammatic approach to categorification of quantum groups I
• Knot homology via derived categories of coherent sheaves II, sl(m) case
• Categorical geometric skew Howe duality

Cited by in corpus (15)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• An introduction to diagrammatic algebra and categorified quantum sl(2)
• Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions
• Braiding via geometric Lie algebra actions
• An odd categorification of quantum sl(2)
• Vertex operators and 2-representations of quantum affine algebras
• Clasp technology to knot homology via the affine Grassmannian
• An approach to categorification of Verma modules
• A quantum Mirković-Vybornov isomorphism
• Equivalences and stratified flops
• Categorification via blocks of modular representations for sl(n)
• A Categorical Quantum Toroidal Action on Hilbert Schemes
• A categorical sl_2 action on some moduli spaces of sheaves
• Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops
• Deformation of tilting-type derived equivalences for crepant resolutions