Equivariant <i>K</i>-Theory Classes of Matrix Orbit Closures

Abstract The group $G = \textrm{GL}_r(k) \times (k^\times )^n$ acts on $\textbf{A}^{r n}$, the space of $r$-by-$n$ matrices: $\textrm{GL}_r(k)$ by row operations and $(k^\times scales columns. A matrix orbit closure is Zariski a point for this action. We prove that class such an in $G$-equivariant $K$-theory n}$ determined matroid generic point. present two formulas class. key to proof show closures have rational singularities.