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arXiv · 2507.18579

Invariants of the finite orthogonal groups in odd dimension and even characteristic

H. E. A. Campbell·R. J. Shank·D. L. Wehlau
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Abstract

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.

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H. E. A. Campbell, R. J. Shank, D. L. Wehlau. 2025-07-24. Invariants of the finite orthogonal groups in odd dimension and even characteristic. https://doi.org/10.1112/jlms.70597

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