On enumerating factorizations in reflection groups

Douvropoulos, Theo

doi:10.5802/alco.261

Douvropoulos, Theo ¹

¹ University of Massachussets at Amherst Department of Mathematics and Statistics

Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 359-385.

Abstract

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

Received: 2020-12-02
Revised: 2022-02-28
Accepted: 2022-08-07
Published online: 2023-05-03

DOI: 10.5802/alco.261

Classification: 05A15, 05E99, 20C08, 20F55
Keywords: factorization enumeration, full twist, regular elements, Frobenius lemma

Author's affiliations:

Douvropoulos, Theo ¹

¹ University of Massachussets at Amherst Department of Mathematics and Statistics

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Douvropoulos, Theo. On enumerating factorizations in reflection groups. Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 359-385. doi : 10.5802/alco.261. https://alco.centre-mersenne.org/articles/10.5802/alco.261/

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