Weyl group action on weight zero Mirković-Vilonen cycles and equivariant multiplicities

Mirković-Vilonen cycles are certain algebraic cycles in the affine Grassmannian that give rise to a particular weight basis (the MV basis) under the Geometric Satake equivalence. I will state a conjecture about the Weyl group action on weight-zero MV cycles and equivariant multiplicities. I can prove it for small coweights in type A. Equivalently, I show that the MV basis agrees with the Springer basis. I have similar results for the Ginzburg-Nakajima basis. A primary tool is work of Braverman, Gaitsgory and Vybornov.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Monday, December 10, 2018 - 14:00 to 15:30
Location: 
Sky Room
Room #: 
394