Thom modules and pseudoreflection groups
Let \(R^*\) be an unstable algebra over the mod p Steenrod algebra \({\mathcal A}^*\). A Thom module over \(R^*\) is defined to be an \(R^*\)-module M which is free of rank 1 and has a compatible \({\mathcal A}^*\)-action. In particular, the cohomology of the Thom space of an oriented vector bundle is a Thom module over the cohomology of the base space. In analogy with work of \textit{R. Stanley} [J. Algebra 49, 134-148 (1977; Zbl 0383.20029)], the authors construct a Thom module associated to a linear character of a subgroup of \(GL_ n({\mathbb{F}}_ p)\) generated by pseudoreflections. They also give a criterion involving Pontryagin classes for such Thom modules to come from vector bundles.
unstable algebra over the mod p Steenrod algebra
scientific article; zbMATH DE number 4119242
scientific article