Evaluation and normalization of Jack superpolynomials

Abstract

Two evaluation formulas are derived for the Jack superpolynomials. The evaluation formulas are expressed in terms of products of fillings of skew diagrams. One of these formulas is nothing but the evaluation formula of the Jack polynomials with prescribed symmetry, which thereby receives here a remarkably simple formulation. Among the auxiliary results required to establish the evaluation formulas, the determination of the conditions ensuring the non-vanishing coefficients in a Pieri-type rule for Jack superpolynomials is worth pointing out. An important application of the evaluation formulas is a new derivation of the combinatorial norm of the Jack superpolynomials. We finally mention that the introduction of a simpler version of the dominance ordering on superpartitions is fundamental to establish our results.

42 pages, 10 figures. v2: minor corrections in Eqs (16) and (17)

References in corpus (1)

• N=4 superconformal Calogero models

Cited by in corpus (16)

• The supersymmetric Ruijsenaars-Schneider model
• Superconformal field theory and Jack superpolynomials
• Macdonald polynomials in superspace: conjectural definition and positivity conjectures
• The first positive rank and crank moments for overpartitions
• The super-Virasoro singular vectors and Jack superpolynomials relationship revisited
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• Schur Superpolynomials: Combinatorial Definition and Pieri Rule
• Ramond singular vectors and Jack superpolynomials
• Supersymmetric polynomials and algebro-combinatorial duality
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Pieri rules for the Jack polynomials in superspace and the 6-vertex model
• Super-Whittaker vector at c=3/2
• Double Macdonald polynomials as the stable limit of Macdonald superpolynomials
• Hopf algebra structure of symmetric and quasisymmetric functions in superspace
• The N=2 supersymmetric Calogero-Sutherland model and its eigenfunctions