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06/11/2020, 17:00 — 18:00 Europe/Lisbon —
Online

Marco Mackaay, *University of Algarve*

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The double-centralizer theorem in 2-representation theory and its applications

Finitary birepresentation theory of finitary bicategories is a categorical analog of finite-dimensional representation theory of finite-dimensional algebras. The role of the simples is played by the so-called simple transitive birepresentations and the classification of the latter, for any given finitary bicategory, is a fundamental problem in finitary birepresentation theory (the classification problem).

After briefly reviewing the basics of birepresentation theory, I will explain an analog of the double centralizer theorem for finitary bicategories, which was inspired by Etingof and Ostrik's double centralizer theorem for tensor categories. As an application, I will show how it can be used to (almost completely) solve the classification problem for Soergel bimodules in any finite Coxeter type.

Projecto FCT `UIDB/04459/2020`.