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. The main tool is work of Braverman, Gaitsgory and Vybornov.

Dinakar Muthiah is an American mathematician. He earned his doctorate in 2013 from Brown University under the supervision of Alexander Braverman. He is currently working at the Kavli Institute for the Physics and Mathematics of the Universe as a Project Researcher. His research is broadly concerned with the geometry of loop groups and double loop groups.