Algebra Seminar: Patimo -- p-hybrid bases of the Hecke algebra

Leonardo Patimo (University of Freiburg) 

Friday 28 February, 12-1pm, Place: Carslaw 275 

Title: p-hybrid bases of the Hecke algebra 

Abstract: In the Hecke algebra of a Weyl group, for every parabolic subgroup one can
define a hybrid basis that "interpolates" between the standard basis and the
Kazhdan-Lusztig basis.  Geometrically these bases can be obtained via hyperbolic
localisation of perverse sheaves.  We will see that in the modular setting we can obtain
similar results using parity sheaves, leading to the construction of new p-hybrid bases
with remarkable positivity properties.  We will conclude by discussing some applications
of these new bases.  This is joint work with Thorge Jensen.