2016
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The 2-representation theory of Soergel bimodules 2-Representations of monoidal categories and 2-categories are categorical analogues of representations of algebras. Well known examples show up in the context of categorified quantum groups, Category O and Soergel bimodules (the latter giving categorifications of Hecke algebras). More recently, Mazorchuk and Miemietz have started to develop a theory of 2-representations, in an attempt to study them more systematically. One (difficult) question that naturally arises for any given monoidal category or 2-category (satisfying some technical conditions), is the classification of its “categorical irreducible representations", the so called simple transitive 2-representations. In a joint paper with Kildetoft, Mazorchuk and Zimmermann and another one with Tubbenhauer, we obtained a complete classification of all simple transitive 2-representations of the so called “small quotient” of the monoidal category of Soergel bimodules, for any finite Coxeter type. In my talk, I will first explain some of the general ideas in 2-representation theory and then illustrate them by focusing on the 2-representation theory of the monoidal category of Soergel bimodules. |