Logarithmic forms and anti-invariant forms of reflection groups

Abstract

Let W be a finite group generated by unitary reflections and A be the set of reflecting hyperplanes. We will give a characterization of the logarithmic differential forms with poles along A in terms of anti-invariant differential forms. If W is a Coxeter group defined over the real numbers, then the characterization provides a new method to find a basis for the module of logarithmic differential forms out of basic invariants.