Braiding via geometric Lie algebra actions

Abstract

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.

40 pages

References in corpus (6)

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• Coherent sheaves and categorical sl(2) actions
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• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Curved Rickard complexes and link homologies
• Categorification of the internal braid group action for quantum groups I: 2-functoriality
• A braid group action on a $p$-DG homotopy category