University of Sydney Algebra Seminar
Joseph Baine
Friday 27 September, 12-1pm, Place: Carslaw 275
(Co)Minuscule Hecke Categories
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.