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