Speaker : Sheng-Fu Chiu (Institute of Mathematics, Academia Sinica)
Title : Koszul duality for the Hecke category
Time : 2021-03-05 (Fri) 13:00 - 14:30
Place : Seminar Room 638, Institute of Mathematics (NTU Campus)
Abstract: This is a special episode of Soergel bimodule theory. Koszul duality for algebras is a special pattern of equivalences between the derived categories of modules over them, which relies on the graded algebra structure and produces extra differential graded structure on the dual side. Moreover, in Lie representation theory this duality is expected to intertwine simple objects with tilting objects on each side of Langlands dual realizations and vice versa. In this talk I will give a brief introduction to Koszul duality for the Hecke category we have studied since last semester. I will start with a natural hidden symmetry of the Hecke algebra and describe how to categorify this symmetry to the level of derived equivalences (that correspond to categorical Koszul duality) between the categories of Soergel bimodules under the setting of Cartan realizations.