On enumerating factorizations in reflection groups

2018/11/15 by Douvropoulos, Theo · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1811.06566

Abstract

We describe an approach, via Malle's permutation Ψ on the set of irreducible characters Irr(W), that gives a uniform derivation of the Chapuy-Stump formula for the enumeration of reflection factorizations of the Coxeter element. It also recovers its weighted generalization by delMas, Reiner, and Hameister, and further produces structural results for factorization formulas of arbitrary regular elements.

Cited by

• Counting factorizations of Singer cycles in linear and unitary groups
• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements

Related

• "Case-free" derivation for Weyl groups of the number of reflection factorisations of a Coxeter element
• A refined count of Coxeter element factorizations
• Polynomiality of factorizations in reflection groups
• Hurwitz numbers for reflection groups III: Uniform formulas
• A note on non-reduced reflection factorizations of Coxeter elements