Equivariant K-Theory Classes of Matrix Orbit Closures. (2nd June 2021) - Berget, Andrew; Fink, Alex
Abstract: The group G = GL_r(k) × (k^× )^n acts on A^r × n, the space of r -by-n matrices: GL_r(k) acts by row operations and (k^× )^n scales columns. A matrix orbit closure is the Zariski closure of a point orbit for this action. We prove that the class of such an orbit closure in G -equivariant K -theory of A^r × n is determined by the matroid of a generic point. We present two formulas for this class. The key to the proof is to show that matrix orbit closures have rational singularities.