Modules with good filtration and invariant theory
type: Item
instance of: scholarly article
zbMATH Open document ID: 0993.16018
publication date: 2002-06-04T00:00:00Z
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 16G20
zbMATH DE Number: 1683639
zbMATH Keywords: simultaneous conjugation
zbMATH Keywords: tilting modules
zbMATH Keywords: exterior powers
zbMATH Keywords: characteristic polynomials
zbMATH Keywords: general linear groups
zbMATH Keywords: rings of invariants
zbMATH Keywords: modules with good filtrations
zbMATH Keywords: representations of quivers
author: A. N. Zubkov
MaRDI profile type: Publication
title: Modules with good filtration and invariant theory
review text: It is a well known theorem of Yu. P. Razmyslov and C. Procesi that all identities with trace of \(n\times n\) matrices over a characteristic zero base field follow from the Cayley-Hamilton identity. This result provides a description of the relations between generators of the ring of invariants of \(m\)-tuples of \(n\times n\) matrices, with respect to the simultaneous conjugation action of the general linear group. A characteristic free generalization was proved by the author [in Algebra Logika 35, No. 4, 433-457 (1996); translation in Algebra Logic 35, No. 4, 241-254 (1996; Zbl 0941.16012)], using results of S. Donkin on modules with good filtration. The present survey outlines this result and the techniques used in its proof. Related works of the author on polynomial invariants of representations of quivers and adjoint action invariants of other classical groups are also discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00049].
reviewed by: Matyas Domokos
description: scientific article; zbMATH DE number 1683639