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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20428 |
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| _version_ | 1866908446902714368 |
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| author | Gan, Wee Liang Ta, Khoa |
| author_facet | Gan, Wee Liang Ta, Khoa |
| contents | Let $FI$ be a skeleton of the category of finite sets and injective maps, and $FI^m$ the product of $m$ copies of $FI$. We prove that if an $FI^m$-module is generated in degree $\leqslant d$ and related in degree $\leqslant r$, then its regularity is bounded above by a function of $m$, $d$, and $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounding regularity of $FI^m$-modules Gan, Wee Liang Ta, Khoa Representation Theory Let $FI$ be a skeleton of the category of finite sets and injective maps, and $FI^m$ the product of $m$ copies of $FI$. We prove that if an $FI^m$-module is generated in degree $\leqslant d$ and related in degree $\leqslant r$, then its regularity is bounded above by a function of $m$, $d$, and $r$. |
| title | Bounding regularity of $FI^m$-modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2407.20428 |