Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909494974349312 |
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| author | Yang, Chenglang |
| author_facet | Yang, Chenglang |
| contents | The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook-lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In this paper, we prove the general cases of Amdeberhan's conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures Yang, Chenglang Combinatorics Mathematical Physics Representation Theory The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook-lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In this paper, we prove the general cases of Amdeberhan's conjectures. |
| title | Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures |
| topic | Combinatorics Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2404.01973 |