Hyperdéterminant d’un SL 2 -homomorphisme
[Hyperdeterminant of an SL 2 -homomorphism]
Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 81-86.

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.

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.

DOI: 10.5802/ambp.240
Classification: 14L30
Keywords: Hyperdeterminant, Steinerbundles, SL 2 modules
Jean Vallès 1

1 Laboratoire de Mathématiques Pures et Appliquées Université de Pau et des Pays de l’Adour 64000 PAU FRANCE
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Jean Vallès. Hyperdéterminant d’un $SL_{2}$-homomorphisme. Annales mathématiques Blaise Pascal, Volume 15 (2008) no. 1, pp. 81-86. doi : 10.5802/ambp.240. https://ambp.centre-mersenne.org/articles/10.5802/ambp.240/

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