Invariants of the finite orthogonal groups in odd dimension and even characteristic
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| Format: | Preprint |
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2025
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| _version_ | 1866913959070662656 |
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| author | Campbell, H. E. A. Shank, R. J. Wehlau, D. L. |
| author_facet | Campbell, H. E. A. Shank, R. J. Wehlau, D. L. |
| contents | We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the generators. This ring of invariants is shown to be a complete intersection and thus is Cohen-Macaulay. This extends the previous computation of Kropholler, Mohseni Rajaei, and Segal valid over the field of order 2. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants of the finite orthogonal groups in odd dimension and even characteristic Campbell, H. E. A. Shank, R. J. Wehlau, D. L. Commutative Algebra 13A50 (Primary) 20F55 (Secondary) We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the generators. This ring of invariants is shown to be a complete intersection and thus is Cohen-Macaulay. This extends the previous computation of Kropholler, Mohseni Rajaei, and Segal valid over the field of order 2. |
| title | Invariants of the finite orthogonal groups in odd dimension and even characteristic |
| topic | Commutative Algebra 13A50 (Primary) 20F55 (Secondary) |
| url | https://arxiv.org/abs/2507.18579 |