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.