PIRSA:18120011

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

Muthiah, D. (2018). Weyl group action on weight zero Mirković-Vilonen cycles and equivariant multiplicities. Perimeter Institute. https://pirsa.org/18120011

Muthiah, Dinakar. Weyl group action on weight zero Mirković-Vilonen cycles and equivariant multiplicities. Perimeter Institute, Dec. 10, 2018, https://pirsa.org/18120011 

          @misc{ pirsa_PIRSA:18120011,
            doi = {10.48660/18120011},
            url = {https://pirsa.org/18120011},
            author = {Muthiah, Dinakar},
            keywords = {Mathematical physics},
            language = {en},
            title = { Weyl group action on weight zero Mirkovi{\'c}-Vilonen cycles and equivariant multiplicities},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {dec},
            note = {PIRSA:18120011 see, \url{https://pirsa.org}}
          }

Dinakar Muthiah

University of Alberta

Talk number
PIRSA:18120011
Collection
Talk Type
Subject
Abstract

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.