A normalization formula for the Jack polynomials in superspace and an identity on partitions
Combinatorics
2008-03-31 v1
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.
Cite
@article{arxiv.0803.4182,
title = {A normalization formula for the Jack polynomials in superspace and an identity on partitions},
author = {Luc Lapointe and Yvan Le Borgne and Philippe Nadeau},
journal= {arXiv preprint arXiv:0803.4182},
year = {2008}
}
Comments
20 pages, 7 figures