Generalized orbital varieties for Mirkovic-Vybornov slices as affinizations of Mirkovic-Vilonen cycles

Abstract

We show that generalized orbital varieties for Mirkovic-Vybornov slices can be indexed by semi-standard Young tableaux. We also check that the Mirkovic-Vybornov isomorphism sends generalized orbital varieties to (dense subsets of) Mirkovic-Vilonen cycles, such that the (combinatorial) Lusztig datum of a generalized orbital variety, which it inherits from its tableau, is equal to the (geometric) Lusztig datum of its MV cycle.

References in corpus (3)

• Instanton moduli spaces and $\mathcal{W}$-algebras
• On generalized category $\mathcal{O}$ for a quiver variety
• Quiver varieties and quantum Knizhnik--Zamolodchikov equation