New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
Journal article, 2024

The super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are polynomials in n+ m variables, which reduce to the Jack polynomials when n= 0 or m= 0 and provide joint eigenfunctions of the quantum integrals of the deformed trigonometric Calogero–Moser–Sutherland system. We prove that the super-Jack polynomials are orthogonal with respect to a bilinear form of the form (p, q) ↦ (Lpq) (0) , with Lp quantum integrals of the deformed rational Calogero–Moser–Sutherland system. In addition, we provide a new proof of the Lassalle–Nekrasov correspondence between deformed trigonometric and rational harmonic Calogero–Moser–Sutherland systems and infer orthogonality of super-Hermite polynomials, which provide joint eigenfunctions of the latter system.

Lassalle–Nekrasov correspondence

Orthogonal polynomials

Super-Jack polynomials

Calogero–Moser–Sutherland systems


Martin Hallnäs

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Constructive Approximation

0176-4276 (ISSN) 1432-0940 (eISSN)

Vol. 59 1 113-142

Quasi-invariants of finite Coxeter groups and integrable systems

Swedish Research Council (VR) (2018-04291), 2019-01-01 -- 2022-12-31.

Subject Categories

Algebra and Logic


Mathematical Analysis



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3/7/2024 9