Plethystic Murnaghan-Nakayama rule via vertex operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915735982309376 |
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| author | Cao, Yue Jing, Naihuan Liu, Ning |
| author_facet | Cao, Yue Jing, Naihuan Liu, Ning |
| contents | Based on the vertex operator realization of the Schur functions, a determinant-type plethystic Murnaghan--Nakayama rule is obtained and utilized to derive a general formula of the expansion coefficients of $s_ν$ in the plethysm product $(p_{n}\circ h_{k})s_μ$. Meanwhile, the equivalence between our algebraic rule and the combinatorial one is also established. As an application, we provide a simple way to compute the generalized Waring formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08412 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Plethystic Murnaghan-Nakayama rule via vertex operators Cao, Yue Jing, Naihuan Liu, Ning Combinatorics Primary: 05E10, 05E05, Secondary: 17B69 Based on the vertex operator realization of the Schur functions, a determinant-type plethystic Murnaghan--Nakayama rule is obtained and utilized to derive a general formula of the expansion coefficients of $s_ν$ in the plethysm product $(p_{n}\circ h_{k})s_μ$. Meanwhile, the equivalence between our algebraic rule and the combinatorial one is also established. As an application, we provide a simple way to compute the generalized Waring formula. |
| title | Plethystic Murnaghan-Nakayama rule via vertex operators |
| topic | Combinatorics Primary: 05E10, 05E05, Secondary: 17B69 |
| url | https://arxiv.org/abs/2212.08412 |