Orthogonality of Jack polynomials in superspace

Abstract

Jack polynomials in superspace, orthogonal with respect to a ``combinatorial'' scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to an ``analytical'' scalar product, introduced in hep-th/0209074 as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an extra parameter) the theory of classical symmetric functions in superspace developed recently in math.CO/0509408

22 pages, this supersedes the second part of math.CO/0412306; (v2) 24 pages, title and abstract slightly modified, minor changes, typos corrected

References in corpus (6)

• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Jack polynomials in superspace
• Classical symmetric functions in superspace
• Superanalogs of the Calogero operators and Jack polynomials
• Jack superpolynomials, superpartition ordering and determinantal formulas

Cited by in corpus (20)

• The supersymmetric Ruijsenaars-Schneider model
• Superconformal field theory and Jack superpolynomials
• Evaluation and normalization of Jack superpolynomials
• Macdonald polynomials in superspace: conjectural definition and positivity conjectures
• 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
• Macdonald polynomials in superspace as eigenfunctions of commuting operators
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• 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
• Nonsymmetric Macdonald Superpolynomials
• Super-Whittaker vector at c=3/2
• Jack polynomials with prescribed symmetry and some of their clustering properties
• The N=2 supersymmetric Calogero-Sutherland model and its eigenfunctions
• A Superpolynomial Version of Nonsymmetric Jack Polynomials
• A normalization formula for the Jack polynomials in superspace and an identity on partitions
• On the Hopf superalgebra of symmetric functions in superspace
• Hopf algebra structure of symmetric and quasisymmetric functions in superspace
• N>=2 symmetric superpolynomials