Matrix invariants of binary forms
type: Item
instance of: scholarly article
title: Matrix invariants of binary forms
zbMATH Open document ID: 0838.16028
author: D. Tambara
published in: Hokkaido Mathematical Journal
publication date: 1996-05-29T00:00:00Z
review text: Let \(k\) be a field of characteristic 0, let \(S=k[x_1,x_2]\) be the polynomial ring in two commuting indeterminates \(x_1\), \(x_2\), and let \(S_n\) be the vector space given by the homogeneous part of \(S\) of degree \(n\). The group \(\text{SL}_2\) acts on \(S\) canonically and the \(\text{SL}_2\)-invariant polynomial maps from the space \(S_d\) to the matrix algebra \(\text{End }S_n\) form an algebra \(A_d(n)\) by matrix multiplication. \(A_d(0)\) is the algebra of invariants of the \(d\)-ic form of classical invariant theory. This paper shows that \(A_d(n)\) is a deformation of a factor of the algebra of covariants of the \(d\)-ic form. Consequently, generators for \(A_d(n)\) can be derived from the generators for the algebra of covariants.
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16S80
zbMATH DE Number: 808301
zbMATH Keywords: binary forms
zbMATH Keywords: Clebsch-Gordan rule
zbMATH Keywords: \(SL_ 2\)-invariant polynomial maps
zbMATH Keywords: matrix algebras
zbMATH Keywords: algebra of invariants
zbMATH Keywords: deformations
zbMATH Keywords: generators
zbMATH Keywords: algebra of covariants
reviewed by: John Clark
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1380892598
OpenAlex ID: W2080105955
DOI: 10.14492/HOKMJ/1380892598
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description: scientific article; zbMATH DE number 808301