  Let $G$ be a reflection group acting on a vector space $V$ (over a field with
zero characteristic). We denote by $S(V^*)$ the coordinate ring of $V$, by $M$
a finite dimensional $G$-module and by $\chi$ a one-dimensional character of
$G$. In this article, we define an algebra structure on the isotypic component
associated to $\chi$ of the algebra $S(V^*) \otimes \Lambda(M^*)$. This
structure is then used to obtain various generalizations of usual criterions on
regularity of integers.
