The quantum K-theory ring of a smooth projective variety is a deformation of its K-theory ring of vector bundles. Inspired by supersymmetric gauge theory and generalizing a result of Gu, Mihalcea, Sharpe, and Zou for Grassmannians, we give conjectural relations in the quantum K-theory rings of partial flag varieties that deform Whitney relations. If these relations hold, then they form a complete set of relations. We prove these relations for Fl(1,n-1;n) relying on the proof of a quantum K divisor axiom conjectured by Buch and Mihalcea for partial flag varieties. I will discuss the geometry of the quantum K divisor axiom and a few other implications of it.
This talk is partly based on joint work with Gu, Mihalcea, Sharpe, Zhang, and Zou.
This video is part of the University of Georgia‘s Algebra seminar.
