Braiding via geometric Lie algebra actions

Details Braiding via geometric Lie algebra actions Braiding via geometric Lie algebra actions

2010-01-05

arxiv.org/abs/1001.0619v4

Mathematics

Algebraic Geometry

40 pages

Scientific paper

We introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra. The same proof shows that strong categorical actions in the sense of Khovanov-Lauda and Rouquier also lead to braid group actions. As an example, we construct a braid group action on derived categories of coherent sheaves on cotangent bundles to partial flag varieties.

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