On the decomposability of mod 2 cohomological invariants of Weyl groups

Christian Hirsch*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)765-809
Number of pages45
JournalCommentarii Mathematici Helvetici
Issue number4
Publication statusPublished - 2020


  • Weyl groups
  • cohomological invariants
  • torsor
  • splitting principle

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