Parity sheaves on the affine Grassmannian and the Mirković-Vilonen conjecture

2013/05/08 by Achar, Pramod N., Rider, Laura
#FOS: Mathematics #Primary 22E57 #Representation Theory (math.RT) #Secondary 14F05

paper · doi:10.48550/arxiv.1305.1684

Abstract

We prove the Mirković-Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau-Mautner-Williamson theory of parity sheaves.

Related

• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Non-perverse parity sheaves on the flag variety
• On torsion in the intersection cohomology of Schubert varieties
• Modular representations of reductive groups and geometry of affine Grassmannians
• Résolutions de Demazure affines et formule de Casselman-Shalika géométrique