On classical invariant theory and binary cubics
Annales de l'Institut Fourier, Volume 37 (1987) no. 3, pp. 191-216.

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

Soit G un groupe algébrique complexe réductif et C[mV] G l’algèbre des polynômes G-invariants sur la somme directe de m copies de l’espace de représentation V de G. Il existe un nombre entier n=n(V) minimal tel que les générateurs et relations de C[mv] G puissent s’obtenir à partir de ceux de C[nv] G par polarisation et restitution pour chaque m>n. On borne n et les degrés des générateurs et relations de C[nV] G , en étendant des résultats de Vust. Ces techniques sont alors appliquées au calcul des invariants de plusieurs formes binaires cubiques.

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Schwarz, Gerald W. On classical invariant theory and binary cubics. Annales de l'Institut Fourier, Volume 37 (1987) no. 3, pp. 191-216. doi : 10.5802/aif.1104. https://aif.centre-mersenne.org/articles/10.5802/aif.1104/

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