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Journal Articles The Electronic Journal of Combinatorics Year : 2009

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

Luc Lapointe
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Abstract

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.
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Dates and versions

hal-00395133 , version 1 (15-06-2009)

Identifiers

  • HAL Id : hal-00395133 , version 1

Cite

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⟩

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