Circuits and Hurwitz action in finite root systems

Joel Brewster Lewis, Victor Reiner

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In a finite real reection group, two factorizations of a Coxeter element into an arbitrary number of reections are shown to lie in the same orbit under the Hurwitz action if and only if they use the same multiset of conjugacy classes. The proof makes use of a surprising lemma, derived from a classification of the minimal linear dependences (matroid circuits) in finite root systems: any set of roots forming a minimal linear dependence with positive coefficients has a disconnected graph of pairwise acuteness.

Original languageEnglish (US)
Pages (from-to)1457-1486
Number of pages30
JournalNew York Journal of Mathematics
StatePublished - 2016

Bibliographical note

Funding Information:
This work was partially supported by NSF grants DMS-1148634 and DMS-1401792.


  • Acuteness
  • Circuit
  • Coxeter element
  • Factorization
  • Gram matrix
  • Hurwitz action
  • Matroid
  • Reection
  • Reection group
  • Root system

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