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

2025/07/24 by H. E. A. Campbell, Campbell, H. E. A., R. J. Shank +3
Mathematics · #13A50 (Primary) 20F55 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A50 #msc:20F55

paper · pdf · doi:10.48550/arxiv.2507.18579

published as J. London. Math.Soc. (2) 2026;E70597 · 27 pages

arxiv created 2025/07/24 · arxiv updated 2026/08/03

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.

Citations

• Invariants of Finite Orthogonal Groups of Plus Type in Odd Characteristic

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