A Normalization Formula for the Jack Polynomials in Superspace and an Identity on Partitions

Yvan Le Borgne (1) , Luc Lapointe , Philippe Nadeau (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 Universität Wien = University of Vienna

We prove a conjecture of Desrosiers, Lapointe and Mathieu giving a closed form formula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the final step of the proof appears an identity on weighted sums of partitions that we demonstrate using the methods of Gessel-Viennot.

Domaines: Combinatoire [math.CO]

Yvan Le Borgne, Luc Lapointe, Philippe Nadeau. A Normalization Formula for the Jack Polynomials in Superspace and an Identity on Partitions. The Electronic Journal of Combinatorics, 2009, 16 (1), pp.R70. ⟨hal-00395133⟩