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 language||English (US)|
|Number of pages||30|
|Journal||New York Journal of Mathematics|
|State||Published - 2016|
Bibliographical noteFunding Information:
This work was partially supported by NSF grants DMS-1148634 and DMS-1401792.
- Coxeter element
- Gram matrix
- Hurwitz action
- Reection group
- Root system