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New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence

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Main Author: Martin, Hallnäs
Format: Book
Language:English
Published: Springer 2023
Subjects:
The super-Jack polynomials
Calogero–Moser–Sutherland system
Online Access:https://link.springer.com/article/10.1007/s00365-023-09636-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7636
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spelling oai:localhost:PNK-76362023-04-06T04:42:44Z New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence Martin, Hallnäs The super-Jack polynomials Calogero–Moser–Sutherland system CC BY 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. 2023-04-06T04:42:44Z 2023-04-06T04:42:44Z 2023 Book https://link.springer.com/article/10.1007/s00365-023-09636-2 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7636 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic The super-Jack polynomials
Calogero–Moser–Sutherland system
spellingShingle The super-Jack polynomials
Calogero–Moser–Sutherland system
Martin, Hallnäs
New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
description CC BY
format Book
author Martin, Hallnäs
author_facet Martin, Hallnäs
author_sort Martin, Hallnäs
title New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
title_short New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
title_full New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
title_fullStr New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
title_full_unstemmed New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
title_sort new orthogonality relations for super-jack polynomials and an associated lassalle–nekrasov correspondence
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00365-023-09636-2
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7636
_version_ 1762456093834870784
score 8.881002

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