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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2303.09605 |
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| _version_ | 1866916085795651584 |
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| author | Henrickson, Graeme Stokke, Anna Wiebe, Max |
| author_facet | Henrickson, Graeme Stokke, Anna Wiebe, Max |
| contents | We give a cyclic sieving phenomenon for symplectic $λ$-tableaux $SP(λ,2m)$, where $λ$ is a partition of an odd integer $n$ and $gcd(m,p)=1$ for any odd prime $p\leq n$. We use the crystal structure on Kashiwara-Nakashima symplectic tableaux to get a cyclic sieving action as the product $σ$ of simple reflections in the Weyl group. The cyclic sieving polynomial is the $q$-anologue of the hook-content formula for symplectic tableaux. More generally, we give a CSP for symplectic skew tableaux with analogous conditions on the shape and a cyclic group action that rotates tableaux weights in a way motivated by the $σ$-action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09605 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A cyclic sieving phenomenon for symplectic tableaux Henrickson, Graeme Stokke, Anna Wiebe, Max Combinatorics 05E18, 05E05 We give a cyclic sieving phenomenon for symplectic $λ$-tableaux $SP(λ,2m)$, where $λ$ is a partition of an odd integer $n$ and $gcd(m,p)=1$ for any odd prime $p\leq n$. We use the crystal structure on Kashiwara-Nakashima symplectic tableaux to get a cyclic sieving action as the product $σ$ of simple reflections in the Weyl group. The cyclic sieving polynomial is the $q$-anologue of the hook-content formula for symplectic tableaux. More generally, we give a CSP for symplectic skew tableaux with analogous conditions on the shape and a cyclic group action that rotates tableaux weights in a way motivated by the $σ$-action. |
| title | A cyclic sieving phenomenon for symplectic tableaux |
| topic | Combinatorics 05E18, 05E05 |
| url | https://arxiv.org/abs/2303.09605 |