Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities [article]

Dinakar Muthiah
2018 arXiv   pre-print
We state a conjecture about the Weyl group action coming from Geometric Satake on zero-weight spaces in terms of equivariant multiplicities of Mirković-Vilonen cycles. We prove it for small coweights in type A. In this case, using work of Braverman, Gaitsgory and Vybornov, we show that the Mirković-Vilonen basis agrees with the Springer basis. We rephrase this in terms of equivariant multiplicities using work of Joseph and Hotta. We also have analogous results for Ginzburg's Lagrangian construction of sl_n representations.
arXiv:1811.04524v1 fatcat:gtfsbtlapbbypeddsftwvb5sne