New Orthogonality Relations for Super-Jack Polynomials and an Associated Lassalle–Nekrasov Correspondence
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00365-023-09636-2 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7636 |
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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 |