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Article Dans Une Revue J.Algebra Année : 2022

Counting chains in the noncrossing partition lattice via the W-Laplacian

Theo Douvropoulos
  • Fonction : Auteur

Résumé

We give an elementary, case-free, Coxeter-theoretic derivation of the formula hnn!/|W| for the number of maximal chains in the noncrossing partition lattice NC(W) of a real reflection group W. Our proof proceeds by comparing the Deligne-Reading recursion with a parabolic recursion for the characteristic polynomial of the W-Laplacian matrix considered in our previous work. We further discuss the consequences of this formula for the geometric group theory of spherical and affine Artin groups.

Dates et versions

hal-03645809 , version 1 (19-04-2022)

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Citer

Guillaume Chapuy, Theo Douvropoulos. Counting chains in the noncrossing partition lattice via the W-Laplacian. J.Algebra, 2022, 602, pp.381-404. ⟨10.1016/j.jalgebra.2022.02.023⟩. ⟨hal-03645809⟩
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