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arXiv · 1811.06566

On enumerating factorizations in reflection groups

Theo Douvropoulos
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Abstract

We describe an approach, via Malle's permutation $Ψ$ on the set of irreducible characters $\text{Irr}(W)$, 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.

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Theo Douvropoulos. 2018-11-15. On enumerating factorizations in reflection groups. https://arxiv.org/abs/1811.06566

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