Schur--Weyl Equivalences for Wreath Product Superalgebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911363898540032 |
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| author | Grimley, Lauren Kujawa, Jonathan R. |
| author_facet | Grimley, Lauren Kujawa, Jonathan R. |
| contents | Let $A$ be an associative superalgebra over a field of characteristic zero. Let $n \geq d+1$. The main result of the paper establishes an equivalence of categories between supermodules for the wreath product $ S_{d} \wr A$ and an explicitly defined category of supermodules for the general linear Lie algebra $\mathfrak{gl}_{n}(A)$. We also give an example showing the bound $n \geq d+1$ cannot be improved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schur--Weyl Equivalences for Wreath Product Superalgebras Grimley, Lauren Kujawa, Jonathan R. Representation Theory Primary 17B10, 16G99. Secondary 20B30 Let $A$ be an associative superalgebra over a field of characteristic zero. Let $n \geq d+1$. The main result of the paper establishes an equivalence of categories between supermodules for the wreath product $ S_{d} \wr A$ and an explicitly defined category of supermodules for the general linear Lie algebra $\mathfrak{gl}_{n}(A)$. We also give an example showing the bound $n \geq d+1$ cannot be improved. |
| title | Schur--Weyl Equivalences for Wreath Product Superalgebras |
| topic | Representation Theory Primary 17B10, 16G99. Secondary 20B30 |
| url | https://arxiv.org/abs/2509.18598 |