Modular invariants of a vector and a covector: A proof of a conjecture of Bonnafé and Kemper

Consider a finite dimensional vector space V over a finite field Fq. We give a minimal generating set for the ring of invariants Fq[V⊕V⁎]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 [3, Conjecture 3.1].