A remark on a conjecture of Derksen

Abstract

Let V be a complex representation of a finite group G of order g. Derksen conjectured that the pth syzygies of the invariant ring Sym(V)^G are generated in degrees at most (p+1)g. We point out that a simple application of the theory of twisted commutative algebras -- using an idea due to Weyl -- gives the bound pg^3.

2 pages