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Representation Theory of Symmetric Groups and Categorification

Alexander Kleshchev (University of Oregon and IAS)

Location:  Hill Center Room 705
Date & time: Wednesday, 08 February 2023 at 3:30PM - 4:30PM

Abstract: We discuss modular branching rules of symmetric groups and explain how these results lead naturally to the ideas of higher representation theory/categorification. In particular, we explain how module categories of symmetric groups form a 2-representations of a 2-Kac-Moody category. We discuss applications of higher representation theory to classical representation theory, in particular, to Broue’s Abelian Defect Conjecture for symmetric groups and their double covers. Broue’s Conjecture describes blocks of finite groups with abelian defect groups in terms of local subgroups up to derived equivalence.