Nilpotent representations
type: Item
instance of: scholarly article
title: Nilpotent representations
zbMATH Open document ID: 0901.16010
author: Lieven Le Bruyn
published in: Journal of Algebra
publication date: 1998-09-29T00:00:00Z
full work available at URL: 5126.pdf
review text: 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)].
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 16G20
zbMATH DE Number: 1097704
zbMATH Keywords: nilpotent representations
zbMATH Keywords: Wesselink stratification
zbMATH Keywords: null-cones
zbMATH Keywords: moduli of quiver-representations
zbMATH Keywords: nilpotent matrices
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
OpenAlex ID: W4212861776
cites work: Desingularizations of varieties of nullforms
cites work: Infinite root systems, representations of graphs and invariant theory
cites work: Instability in invariant theory
cites work: MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS
cites work: Q3346437
cites work: Q3686804
cites work: Q3665245
cites work: Q4740026
cites work: A Stratification of the Null Cone Via the Moment Map
cites work: General Representations of Quivers
cites work: Q3993369
DOI: 10.1006/JABR.1997.7122
description: scientific article; zbMATH DE number 1097704