The field of \(U\)-invariants of the adjoint representation of the group \(\mathrm{GL}(n,K)\)
type: Item
instance of: scholarly article
title: The field of \(U\)-invariants of the adjoint representation of the group \(\mathrm{GL}(n,K)\)
zbMATH Open document ID: 1266.13005
DOI: 10.1134/S0001434613010185
author: K. A. Vyatkina
author: A. N. Panov
published in: Mathematical Notes
publication date: 2013-04-26T00:00:00Z
review text: Let \(M\) denote the space of \(n\times n\) matrices over a field \(K\) of characteristic zero. Consider the adjoint action of the general linear group \(\mathrm{GL}(n,K)\) on \(M\), and let \(U\) be the subgroup of unipotent upper triangular matrices in \(\mathrm{GL}(n,K)\). The authors present \(n(n+1)/2\) algebraically independent \(U\)-invariant polynomial functions on \(M\) that generate the field of \(U\)-invariant rational functions on \(M\).
reviewed by: Matyas Domokos
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 6158173
zbMATH Keywords: field of invariants
zbMATH Keywords: adjoint representation
zbMATH Keywords: unitriangular group
MaRDI profile type: Publication
cites work: Invariants of Certain Groups I
cites work: Q5531038
full work available at URL: s0001434613010185
OpenAlex ID: W2045801242
description: scientific article; zbMATH DE number 6158173