Fields of U-invariants of matrix tuples

Abstract

The general linear group $\mathrm{GL}(n)$ acts on the direct sum of $m$ copies of $\mathrm{Mat}(n)$ by the adjoint action. The action of $\mathrm{GL}(n)$ induces the action of the unitriangular subgroup $U$. We present the system of free generators of the field of $U$-invariants.