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arXiv · 0902.1796

Coherent sheaves and categorical sl(2) actions

Sabin Cautis·Joel Kamnitzer·Anthony Licata
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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.

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Sabin Cautis, Joel Kamnitzer, Anthony Licata. 2009-02-11. Coherent sheaves and categorical sl(2) actions. https://doi.org/10.1215/00127094-2010-035

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