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Isaac Newton Institute for Mathematical Sciences

Higher representations of Lie algebras

Author: R Rouquier (University of Oxford)

Abstract

We will introduce monoidal categories associated with complex semi-simple Lie algebras (and more general Kac-Moody algebras). Their actions ("2-representations") on categories can be analyzed. There is a highest weight theory and a classification of "irreducible" cases. Examples of 2-representations include various types of Hecke algebras and sheaves on flag varieties and on quiver varieties.