A refined count of Coxeter element factorizations
Combinatorics
2017-08-22 v1 Representation Theory
Abstract
For well-generated complex reflection groups, Chapuy and Stump gave a simple product for a generating function counting reflection factorizations of a Coxeter element by their length. This is refined here to record the number of reflections used from each orbit of hyperplanes. The proof is case-by-case via the classification of well-generated groups. It implies a new expression for the Coxeter number, expressed via data coming from a hyperplane orbit; a case-free proof of this due to J. Michel is included.
Keywords
Cite
@article{arxiv.1708.06292,
title = {A refined count of Coxeter element factorizations},
author = {Elise delMas and Thomas Hameister and Victor Reiner},
journal= {arXiv preprint arXiv:1708.06292},
year = {2017}
}