Geometry and categorification

Abstract

We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform categorical calculations, and readily relate classical constructions of geometric representation theory to categorical ones.

23 pages. an expository article to appear in "Perspectives on Categorification."

References in corpus (2)

• Yangians and quantizations of slices in the affine Grassmannian
• A categorical action on quantized quiver varieties

Cited by in corpus (1)

• Modules over plane curve singularities in any ranks and DAHA