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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.18268 |
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| _version_ | 1866909549946994688 |
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| author | Zhou, Yue |
| author_facet | Zhou, Yue |
| contents | The Selberg integral, an $n$-dimensional generalization of the Euler beta integral, plays a central role in random matrix theory, Calogero--Sutherland quantum many body systems, Knizhnik--Zamolodchikov equations, and multivariable orthogonal polynomial theory. The Selberg integral is known to be equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a $(p+1)$-component generalization of the $q$-Morris identity. It in turn yields a generalization of the Selberg integral. The $p=1$ case of Baker and Forrester's conjecture was proved by Károlyi, Nagy, Petrov and Volkov in 2015. In this paper, we give a proof of the $(p+1)$-component $q$-Baker--Forrester conjecture, thereby settling this 26-year-old conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A proof of the multi-component $q$-Baker--Forrester conjecture Zhou, Yue Combinatorics 05A30, 33D70 The Selberg integral, an $n$-dimensional generalization of the Euler beta integral, plays a central role in random matrix theory, Calogero--Sutherland quantum many body systems, Knizhnik--Zamolodchikov equations, and multivariable orthogonal polynomial theory. The Selberg integral is known to be equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a $(p+1)$-component generalization of the $q$-Morris identity. It in turn yields a generalization of the Selberg integral. The $p=1$ case of Baker and Forrester's conjecture was proved by Károlyi, Nagy, Petrov and Volkov in 2015. In this paper, we give a proof of the $(p+1)$-component $q$-Baker--Forrester conjecture, thereby settling this 26-year-old conjecture. |
| title | A proof of the multi-component $q$-Baker--Forrester conjecture |
| topic | Combinatorics 05A30, 33D70 |
| url | https://arxiv.org/abs/2503.18268 |