A Mirkovic-Vybornov isomorphism for the Beilinson-Drinfeld Grassmannian, in action

Abstract: In their recent paper on the MV basis and DH measures, Baumann, Kamnitzer and Knutson showed that the MV cycles (named after Mirkovic and Vilonen who used them to put the geometric Satake correspondence on rigorous footing) yield a perfect basis in the coordinate ring of the unipotent subgroup, C[N]. In particular, they showed that the product of two MV basis vectors in C[N] is given by intersection multiplicities appearing in the intersection of the BD degeneration of the product of the corresponding MV cycles with the central fibre. In this talk we describe how the Mirkovic-Vybornov isomorphism can be generalized to give a concrete way to compute such products when G=GL_m. Time permitting we discuss connections to cluster algebras.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar