English

Hurwitz Transitivity of Longer Reflection Factorizations in G4 and G5

Combinatorics 2018-08-06 v1

Abstract

We prove that the Hurwitz action on reflection factorizations of Coxeter elements is transitive up to certain natural constraints in the complex reflection groups G4 and G5. This affirms a more general conjecture by Lewis and Reiner in these specific cases. The proof uses induction on length of the factorization using the fact that the square of a reflection is also a reflection.

Keywords

Cite

@article{arxiv.1808.01268,
  title  = {Hurwitz Transitivity of Longer Reflection Factorizations in G4 and G5},
  author = {Zachery Peterson},
  journal= {arXiv preprint arXiv:1808.01268},
  year   = {2018}
}

Comments

20 pages, one external figure, comments welcomed