English

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.

Keywords

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

R2 v1 2026-06-21T10:25:29.243Z