English

Polynomiality of factorizations in reflection groups

Group Theory 2021-11-30 v2 Algebraic Geometry Combinatorics

Abstract

We study the number of ways of factoring elements in the complex reflection groups G(r,s,n) as products of reflections. We prove a result that compares factorization numbers in G(r,s,n) to those in the symmetric group on n letters, and we use this comparison, along with the ELSV formula, to deduce a polynomial structure for factorizations in G(r,s,n).

Keywords

Cite

@article{arxiv.2004.13213,
  title  = {Polynomiality of factorizations in reflection groups},
  author = {Elzbieta Polak and Dustin Ross},
  journal= {arXiv preprint arXiv:2004.13213},
  year   = {2021}
}

Comments

Minor revisions. To appear in Canadian Journal of Mathematics

R2 v1 2026-06-23T15:08:23.619Z