Hyperdéterminant d’un $SL_{2}$-homomorphisme

Vallès, Jean

Hyperdéterminant d’un

S L_{2}

-homomorphisme

Vallès, Jean

Annales mathématiques Blaise Pascal, Tome 15 (2008), p. 81-86 / Harvested from Numdam

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Résumé
Abstract

Etant donnés $A_{1}, \dots, A_{s}$ ( $s \geq 3$ ) des $S L_{2} (ℂ)$ -modules non triviaux de dimensions respectives $n_{1} + 1 \geq \dots \geq n_{s} + 1$ (avec $n_{1} = n_{2} + \dots + n_{s}$ ) et $φ \in ℒ (A_{2} \otimes \dots \otimes A_{s}, A_{1}^{*})$ un $S L_{2} (ℂ)$ -homomorphisme, nous montrons que l’hyperdéterminant de $φ$ est nul sauf si les modules $A_{i}$ sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.

Let $A_{1}, \dots, A_{s}$ ( $s \geq 3$ ) be non-trivial $S L_{2} (ℂ)$ -modules with dimensions $n_{1} + 1 \geq \dots \geq n_{s} + 1$ (such that $n_{1} = n_{2} + \dots + n_{s}$ ) and $φ \in ℒ (A_{2} \otimes \dots \otimes A_{s}, A_{1}^{*})$ an $S L_{2} (ℂ)$ -homomorphism. We show that the hyperdeterminant of $φ$ is null except if the modules $A_{i}$ are irreducibles and the homomorphism is the multiplication of homogeneous polynomials with two variables.

Publié le : 2008-01-01

MR 2418014 | Zbl 1141.14030

DOI : https://doi.org/10.5802/ambp.240
Classification: 14L30
Mots clés: Hyperdéterminant, fibrés de Steiner,

S L_{2}

modules

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     author = {Vall\`es, Jean},
     title = {Hyperd\'eterminant d'un $SL\_{2}$-homomorphisme},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     year = {2008},
     pages = {81-86},
     doi = {10.5802/ambp.240},
     zbl = {1141.14030},
     mrnumber = {2418014},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2008__15_1_81_0}
}

Vallès, Jean. Hyperdéterminant d’un $SL_{2}$-homomorphisme. Annales mathématiques Blaise Pascal, Tome 15 (2008) pp. 81-86. doi : 10.5802/ambp.240. http://gdmltest.u-ga.fr/item/AMBP_2008__15_1_81_0/

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