On classical invariant theory and binary cubics
Let G be a reductive complex algebraic group, and let \({\mathbb{C}}[mV]^ G\) denote the algebra of invariant polynomial functions on the direct sum of m copies of the representation space V of G. There is a smallest integer \(n=n(V)\) such that generators and relations of \({\mathbb{C}}[mV]^ G\) can be obtained from those of \({\mathbb{C}}[nV]^ G\) by polarization and restitution for all \(m>n\). We bound n and the degrees of generators and relations of \({\mathbb{C}}[nV]^ G\), extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
algebra of invariant polynomial functions
scientific article; zbMATH DE number 3961808
scientific article