The field of \(U\)-invariants of the adjoint representation of the group \(\mathrm{GL}(n,K)\) (Q1947782)

Let \(M\) denote the space of \(n\times n\) matrices over a field \(K\) of characteristic zero. Consider the adjoint action of the general linear group \(\mathrm{GL}(n,K)\) on \(M\), and let \(U\) be the subgroup of unipotent upper triangular matrices in \(\mathrm{GL}(n,K)\). The authors present \(n(n+1)/2\) algebraically independent \(U\)-invariant polynomial functions on \(M\) that generate the field of \(U\)-invariant rational functions on \(M\).