Nilpotent Representations
Copyright policy )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)].
- University of Antwerp Belgium
null-cones, nilpotent matrices, Algebra and Number Theory, Group actions on varieties or schemes (quotients), Trace rings and invariant theory (associative rings and algebras), nilpotent representations, Representations of quivers and partially ordered sets, moduli of quiver-representations, Wesselink stratification
null-cones, nilpotent matrices, Algebra and Number Theory, Group actions on varieties or schemes (quotients), Trace rings and invariant theory (associative rings and algebras), nilpotent representations, Representations of quivers and partially ordered sets, moduli of quiver-representations, Wesselink stratification
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