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On the decomposability of mod 2 cohomological invariants of Weyl groups. (English) Zbl 07310901
Summary: We compute the invariants of Weyl groups in mod 2 Milnor \(K\)-theory and more general cycle modules, which are annihilated by 2. Over a base field of characteristic coprime to the group order, the invariants decompose as direct sums of the coefficient module. All basis elements are induced either by Stiefel-Whitney classes or specific invariants in the Witt ring. The proof is based on Serre’s splitting principle that guarantees detection of invariants on elementary abelian 2-subgroups generated by reflections.
20G10 Cohomology theory for linear algebraic groups
12G05 Galois cohomology
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