Computing fusion products of MV cycles using the Mirkovic–Vybornov isomorphism

Abstract: The fusion of two subvarieties in the affine Grassmannian is a degeneration of their product, defined using the Beilinson-Drinfeld Grassmannian. In this talk, we present a conceptually elementary approach to computing this product in type A when the varieties are MV cycles. As an application, we can compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of $\text{GL}_4$, confirming that all the cluster variables are contained in the basis of MV cycles.

mathematical physicscommutative algebraalgebraic geometryalgebraic topologynumber theoryquantum algebrarings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

PIMS Geometry / Algebra / Physics (GAP) Seminar