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| Main Author: | |
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| Format: | Preprint |
| Published: |
2005
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math-ph/0511015 |
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| _version_ | 1866909469617684480 |
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| author | Langmann, Edwin |
| author_facet | Langmann, Edwin |
| contents | We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_ph_0511015 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | A method to derive explicit formulas for an elliptic generalization of the Jack polynomials Langmann, Edwin Mathematical Physics 82B23, 35Q58, 81Q05 We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case. |
| title | A method to derive explicit formulas for an elliptic generalization of the Jack polynomials |
| topic | Mathematical Physics 82B23, 35Q58, 81Q05 |
| url | https://arxiv.org/abs/math-ph/0511015 |