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

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

2008-03-28

arxiv.org/abs/0803.4182v1

Mathematics

Combinatorics

20 pages, 7 figures

Scientific paper

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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