Coherent sheaves and categorical sl(2) actions
Algebraic Geometry
2019-12-19 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.0902.1796,
title = {Coherent sheaves and categorical sl(2) actions},
author = {Sabin Cautis and Joel Kamnitzer and Anthony Licata},
journal= {arXiv preprint arXiv:0902.1796},
year = {2019}
}
Comments
29 pages