Seminar in Real & Complex Geometry

Wednesday, 30.05.2012, 15:00-16:00, Schreiber building, room 210

Jiuzu Hong, Tel Aviv University

Polynomial functors and categorifications


We categorify various Fock space representations on the algebra of symmetric functions via the category P of strict polynomial functors of finite degree. More precisely, we use the category P to categorify the Fock space representations of type A affine Lie algebra and Heisenberg algebras, and we also categorify the commutativity of the action of the affine Lie algebras and the level p action of Heisenberg algebras on the Fock space. Moreover, we study the relationship between these categorifications and Schur-Weyl duality. The duality is formulated as a functor from the category P to the category of linear species, and we prove that Schur-Weyl duality is a morphism of these categorification structures. In the end, we propose a definition of Hopf category, and we show that the category of polynomial functors is naturally endowed with a Hopf category structure.