Algebra Seminar: Baine -- (Co)Minuscule Hecke Categories

Joseph Baine (USyd) will be speaking in the algebra seminar this week.  Joe will be
presenting the work of his PhD thesis---please come to celebrate his accomplishment! We
will hold a lunch in his honor after the talk, everyone is very welcome to join. 

Where: Carslaw 275 

When: Friday 27 September, 12-1pm 

Title: (Co)Minuscule Hecke Categories 

Abstract: Categories whose Grothendieck groups are isomorphic to a Hecke algebra H or a
H-module are known as Hecke categories.  Two extremely important classes of Hecke
categories are the categories of parity sheaves and mixed tilting sheaves on a (partial)
flag variety.  In this talk we consider these Hecke categories when the partial flag
variety is minuscule or cominuscule.  In particular, we completely determine the
antispherical p-Kazhdan-Lusztig bases in all characteristics, and the spherical
p-Kazhdan-Lusztig bases in good characteristic.  The antispherical 2-Kazhdan-Lusztig
theory of cominuscule Hecke categories is shown to be as complicated as it can be.
These are the only examples (outside dihedral groups) of Hecke categories whose
p-Kazhdan-Lusztig theory can now be said to be understood.