Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde

Hacene Belbachir (1) , Adrien Boussicault (2) , Jean-Gabriel Luque (3, 2)

1 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.

Mots clés: symmetric functions; Hyperdeterminant; Jack polynomials; Vandermonde; symmetric functions.

Domaines: Combinatoire [math.CO]

Hacene Belbachir, Adrien Boussicault, Jean-Gabriel Luque. Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde. Journal of Algebra, 2008, 320 (11), pp.3911-3925. ⟨10.1016/j.jalgebra.2008.06.015⟩. ⟨hal-00173319⟩