Some four-dimensional orthogonal invariants

2025/04/15 by Ren, Shan, Zhang, Runxuan
#13A50 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.10841

Abstract

Let p be an odd prime and \mathbbF_p be the prime field of order p. Consider a 2-dimensional orthogonal group G over \mathbbF_p acting on the standard representation V and the dual space V^*. We compute the invariant ring \mathbbF_p[V⊕ V^*]^G via explicitly exhibiting a minimal generating set. Our method finds an application of s-invariants appeared in covariant theory of finite groups.

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