Generic semistability for reductive group actions (Q2816992)

In this paper the authors continue their study of \textit{generic semistability} begun in a previous paper [\textit{D. Hyeon} and \textit{J. Park}, ``Generic states and stability'', \url{arXiv:1703.02697}]. In the previous work, the authors considered semisimple algebraic groups over a field of characteristic zero -- in this paper they extend to reductive groups. The main result is that for a reductive group \(G\) and a \(G\)-module \(V\), a point \(v\in V\) is generically semistable (\(0\not\in T\cdot v\) for a general maximal torus \(T\)) if and only if it is semistable (in the usual sense) with respect to action of the radical \(R(G)\).