Nilpotent representations
Let \(N_{m,n}\) be the set of \(m\)-tuples of nilpotent \(n\times n\) matrices; this is the nullcone of the action of \(\text{GL}_n\) on \(m\)-tuples of \(n\times n\) matrices by simultaneous conjugation. The author considers the stratification of \(N_{m,n}\) arising from the work of \textit{W. Hesselink} [Invent. Math. 55, 141-163 (1979; Zbl 0401.14006)], which refines the famous Hilbert-Mumford criterion. An algorithm to determine non-empty strata is given; it is based on a reduction to the determination of semi-stable points on a specific quiver-representation problem plus results of \textit{A. Schofield} [Proc. Lond. Math. Soc., III. Ser. 65, No. 1, 46-64 (1992; Zbl 0795.16008)]\ and \textit{A. D. King} [Q. J. Math., Oxf. II. Ser. 45, No. 180, 515-530 (1994; Zbl 0837.16005)].
scientific article; zbMATH DE number 1097704
scientific article