Eigenvalues of Heckman-Polychronakos operators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912539449753600 |
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| author | Dunkl, Charles Gorin, Vadim |
| author_facet | Dunkl, Charles Gorin, Vadim |
| contents | Heckman-Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators $\mathcal D_i$ as $\mathcal P_m= \sum_{i=1}^N (x_i \mathcal D_i)^m$. They have been known since 1990s in connection with trigonometric Calogero-Moser-Sutherland Hamiltonian and Jack symmetric polynomials. We explicitly compute the eigenvalues of these operators for symmetric and skew-symmetric eigenfunctions, as well as partial sums of eigenvalues for general polynomial eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of Heckman-Polychronakos operators Dunkl, Charles Gorin, Vadim Representation Theory Mathematical Physics Classical Analysis and ODEs Combinatorics Heckman-Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators $\mathcal D_i$ as $\mathcal P_m= \sum_{i=1}^N (x_i \mathcal D_i)^m$. They have been known since 1990s in connection with trigonometric Calogero-Moser-Sutherland Hamiltonian and Jack symmetric polynomials. We explicitly compute the eigenvalues of these operators for symmetric and skew-symmetric eigenfunctions, as well as partial sums of eigenvalues for general polynomial eigenfunctions. |
| title | Eigenvalues of Heckman-Polychronakos operators |
| topic | Representation Theory Mathematical Physics Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2412.01938 |