Hyperdéterminant d’un SL 2 -homomorphisme
Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 81-86.

Etant donnés A 1 ,,A s (s3) des SL 2 ()-modules non triviaux de dimensions respectives n 1 +1n s +1 (avec n 1 =n 2 ++n s ) et φ(A 2 A s ,A 1 * ) un SL 2 ()-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 ,,A s (s3) be non-trivial SL 2 ()-modules with dimensions n 1 +1n s +1 (such that n 1 =n 2 ++n s ) and φ(A 2 A s ,A 1 * ) an SL 2 ()-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.

DOI : https://doi.org/10.5802/ambp.240
Classification : 14L30
Mots clés : Hyperdéterminant, fibrés de Steiner, SL 2 modules
@article{AMBP_2008__15_1_81_0,
     author = {Vall\`es, Jean},
     title = {Hyperd\'eterminant d'un $SL\_{2}$-homomorphisme},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {81--86},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {1},
     year = {2008},
     doi = {10.5802/ambp.240},
     mrnumber = {2418014},
     zbl = {1141.14030},
     language = {fr},
     url = {www.numdam.org/item/AMBP_2008__15_1_81_0/}
}
Vallès, Jean. Hyperdéterminant d’un $SL_{2}$-homomorphisme. Annales Mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 81-86. doi : 10.5802/ambp.240. http://www.numdam.org/item/AMBP_2008__15_1_81_0/

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