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Article Dans Une Revue Journal of Algebra Année : 2010

Orbites d'Hurwitz des factorisations primitives d'un élément de Coxeter

Résumé

We study the Hurwitz action of the classical braid group on factorisations of a Coxeter element c in a well-generated complex reflection group W. It is well-known that the Hurwitz action is transitive on the set of reduced decompositions of c in reflections. Our main result is a similar property for the primitive factorisations of c, i.e. factorisations with only one factor which is not a reflection. The motivation is the search for a geometric proof of Chapoton's formula for the number of chains of given length in the non-crossing partitions lattice NCP_W. Our proof uses the properties of the Lyashko-Looijenga covering and the geometry of the discriminant of W.

Dates et versions

hal-00528069 , version 1 (21-10-2010)

Identifiants

Citer

Vivien Ripoll. Orbites d'Hurwitz des factorisations primitives d'un élément de Coxeter. Journal of Algebra, 2010, 323 (5), pp.1432-1453. ⟨10.1016/j.jalgebra.2009.12.010⟩. ⟨hal-00528069⟩
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