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arXiv · 1307.0498

Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]

Joel Kamnitzer
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Abstract

Given a vector space with an action of a semi-simple Lie algebra, we can try to "categorify" this representation, which means finding a category where the generators of the Lie algebra act by functors. Such categorical representations arise naturally in geometric representation theory and in modular representation theory of symmetric groups. A framework for studying categorical representations was introduced by Rouquier and Khovanov-Lauda. Their definitions are algebraic/diagrammatic, but are connected to the topology of quiver varieties by the work of Rouquier and Varagnolo-Vasserot. In this paper, we give a survey of the above circle of ideas.

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Joel Kamnitzer. 2013-07-01. Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]. https://arxiv.org/abs/1307.0498

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