On classical invariant theory and binary cubics

Schwarz, Gerald W.

Annales de l'Institut Fourier, Tome 37 (1987), p. 191-216 / Harvested from Numdam

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Résumé
Abstract

Soit $G$ un groupe algébrique complexe réductif et $C [m V]^{G}$ 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 $C [m v]^{G}$ puissent s’obtenir à partir de ceux de $C [n v]^{G}$ par polarisation et restitution pour chaque $m > n$ . On borne $n$ et les degrés des générateurs et relations de $C [n V]^{G}$ , en étendant des résultats de Vust. Ces techniques sont alors appliquées au calcul des invariants de plusieurs formes binaires cubiques.

Let $G$ be a reductive complex algebraic group, and let $C [m V]^{G}$ 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 $C [m V]^{G}$ can be obtained from those of $C [n V]^{G}$ by polarization and restitution for all $m > n$ . We bound and the degrees of generators and relations of $C [n V]^{G}$ , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.

Publié le : 1987-01-01

MR 89h:14036 | Zbl 0597.14011 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1104

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     author = {Schwarz, Gerald W.},
     title = {On classical invariant theory and binary cubics},
     journal = {Annales de l'Institut Fourier},
     volume = {37},
     year = {1987},
     pages = {191-216},
     doi = {10.5802/aif.1104},
     mrnumber = {89h:14036},
     zbl = {0597.14011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1987__37_3_191_0}
}

Schwarz, Gerald W. On classical invariant theory and binary cubics. Annales de l'Institut Fourier, Tome 37 (1987) pp. 191-216. doi : 10.5802/aif.1104. http://gdmltest.u-ga.fr/item/AIF_1987__37_3_191_0/

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