Coherent sheaves and categorical sl(2) actions

Details Coherent sheaves and categorical sl(2) actions Coherent sheaves and categorical sl(2) actions

2009-02-11

arxiv.org/abs/0902.1796v2

Mathematics

Algebraic Geometry

29 pages

Scientific paper

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.

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