|Location:||MSRI: Simons Auditorium|
The Hecke category is a categorification of the Hecke algebra that plays an important role in geometric representation theory. Using this categorification,
I will introduce a positive characteristic analogue of the famous Kazhdan-Lusztig basis of the Hecke algebra, called the p-canonical or p-Kazhdan-Lusztig basis.
If time permits, I will mention connections between
the p-Kazhdan-Lusztig basis and the representation theory of reductive algebraic groups. Motivated by the very rich theory of Kazhdan-Lusztig cells, I study cells with respect to the p-Kazhdan-Lusztig basis. Throughout the talk, I will use SL_2 as a running example. In the
end, I will give a complete description of p-Cells in finite type A and mention some interesting results in finite types B and C.