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.