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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/2408.16250 |
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| _version_ | 1866908432873816064 |
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| author | Ha, Le Minh Hai, Nguyen Dang Ho Van Nghia, Nguyen |
| author_facet | Ha, Le Minh Hai, Nguyen Dang Ho Van Nghia, Nguyen |
| contents | We verify the conjectures due to Lewis, Reiner and Stanton about the Hilbert series of the invariant ring of the truncated polynomial ring for all parabolic subgroups up to rank $3$. This is done by constructing an explicit set of generators for each invariant ring in question. We also propose a conjecture concerning the action of the Steenrod algebra and the Dickson algebra on a certain naturally occurring filtration of the invariant ring under the general linear group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Modular Invariants of Truncated Polynomial Rings in low ranks Ha, Le Minh Hai, Nguyen Dang Ho Van Nghia, Nguyen Rings and Algebras Algebraic Topology Combinatorics Primary 54C40, 14E20, Secondary 46E25, 20C20 We verify the conjectures due to Lewis, Reiner and Stanton about the Hilbert series of the invariant ring of the truncated polynomial ring for all parabolic subgroups up to rank $3$. This is done by constructing an explicit set of generators for each invariant ring in question. We also propose a conjecture concerning the action of the Steenrod algebra and the Dickson algebra on a certain naturally occurring filtration of the invariant ring under the general linear group. |
| title | On Modular Invariants of Truncated Polynomial Rings in low ranks |
| topic | Rings and Algebras Algebraic Topology Combinatorics Primary 54C40, 14E20, Secondary 46E25, 20C20 |
| url | https://arxiv.org/abs/2408.16250 |