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2 June 2021 Jonathan Brundan - Heisenberg actions on Abelian categories

I will talk about my joint work with Alistair Savage and Ben Webster which develops a general framework for studying actions of the infinite-dimensional Heisenberg Lie algebra on locally finite Abelian categories. The first example comes from Khovanov’s Heisenberg category acting on representations of symmetric groups. In fact, most of the important Abelian categories appearing in “type A” representation theory admit an action by an appropriately defined Heisenberg category, and our approach unifies the study of all of these examples. Time permitting, I hope also to explain a new application of the Heisenberg graphical calculus to another interesting combinatorial category—the partition category.