Representation functors and flag-algebras for the classical groups. II
type: Item
instance of: scholarly article
title: Representation functors and flag-algebras for the classical groups. II
zbMATH Open document ID: 0616.14038
DOI: 10.1016/0021-8693(85)90185-1
author: Glenn Lancaster
author: Jacob Towber
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Previously [see \textit{J. Towber}, J. Algebra 47, 80--104 (1977; Zbl 0358.15033) and part I of this paper, ibid. 59, 16--38 (1979; Zbl 0441.14013)] the authors have constructed functors \(\Lambda^+\) from \(R\)-modules to \(R\)-algebras (\(R\) any commutative ring) such that for \(V\) a finite-dimensional vector space over an algebraically closed field \(R\) of characteristic 0, \(\Lambda^+(V)\) is isomorphic to the coordinate ring \(R[G/U]\) of the base affine space \(G/U\) (\(U\) is a unipotent radical of the Borel subgroup of \(G\)) for classical groups \(G=\mathrm{GL}(V)\), \(G=\mathrm{SO}(V)\) (with odd \(\dim(V)\)) and \(\mathrm{SP}(V)\). In the present paper they complete their program for all classical groups by treating similarly the groups \(\mathrm{SO}(V)\) (with even \(\dim(V)\)) and \(\mathrm{O}(V)\). There still exist results in classical 19th century invariant theory which have never been translated into modern terms. The authors express the hope that one possible application of the functors in the paper under review is providing a form in which such a translation is possible.
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 14L17
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 3997993
zbMATH Keywords: coordinate ring
zbMATH Keywords: base affine space
zbMATH Keywords: classical groups
zbMATH Keywords: invariant theory
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90185-1
OpenAlex ID: W4233423036
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description: scientific article; zbMATH DE number 3997993