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Thom modules and pseudoreflection groups. (English) Zbl 0683.55012

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 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.
Reviewer: R.Steiner

MSC:

55R40 Homology of classifying spaces and characteristic classes in algebraic topology
55R25 Sphere bundles and vector bundles in algebraic topology

Citations:

Zbl 0383.20029
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References:

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