"Case-free" derivation for Weyl groups of the number of reflection factorisations of a Coxeter element

Jean Michel (1)

1 IMJ - Institut de Mathématiques de Jussieu

Chapuy and Stump have given a nice generating series for the number of factorisations of a Coxeter element as a product of reflections. Their method is to evaluate case by case a character-theoretic expression. The goal of this note is to give a uniform evaluation of their character-theoretic expression in the case of Weyl groups, by using combinatorial properties of Deligne-Lusztig representations.

Mots clés: Coxeter element; factorisations; absolute length; dual braid monoid; well-generated complex reflection groups

Domaines: Théorie des représentations [math.RT]; Combinatoire [math.CO]

Jean Michel. "Case-free" derivation for Weyl groups of the number of reflection factorisations of a Coxeter element. 2014. ⟨hal-01052484⟩