TItle: Reflection groups and their invariant mixed forms

Abstract: We consider finite reflection groups containing non-diagonalizable reflections, called transvections, and the associated action on a vector space over a field of positive characteristic. The numerology determined by a Saito criterion describes a hypothetical basis of invariant mixed forms as a free module over the set of invariant polynomials. We provide this criterion and explicitly construct the desired basis from invariant derivations and differential forms for a specific class of reflection groups.