Let Formula: see text be an odd prime and Formula: see text be the prime field of order Formula: see text. Consider a Formula: see text-dimensional orthogonal group Formula: see text over Formula: see text acting on the standard representation Formula: see text and the dual space Formula: see text. We compute the invariant ring Formula: see text via explicitly exhibiting a minimal generating set. Our method provides an application of the Formula: see text-invariants appearing in the covariant theory of finite groups.
Ren et al. (Tue,) studied this question.