Modular Invariants of a Vector and a Covector: a proof of a conjecture of Bonnafé and Kemper

Abstract

Consider a finite dimensional vector space $V$ over a finite field ${\mathbb{F}}_q$. We give a minimal generating set for the ring of invariants ${\mathbb{F}}_q[V\oplus V^{\ast }{]}^{\text{GL}(V)}$, and show that this ring is a Gorenstein ring but is not a complete intersection. These results confirm a conjecture of Bonnafé and Kemper.

arXiv commentA new correct proof of the main theorem is given

Cited by in corpus (1)

• Vector invariants for two-dimensional orthogonal groups over finite fields