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arXiv · 0803.4182

A normalization formula for the Jack polynomials in superspace and an identity on partitions

Luc Lapointe·Yvan Le Borgne·Philippe Nadeau
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Abstract

We prove a previously conjectured 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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Luc Lapointe, Yvan Le Borgne, Philippe Nadeau. 2008-03-28. A normalization formula for the Jack polynomials in superspace and an identity on partitions. https://arxiv.org/abs/0803.4182

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