Non-crossing partitions of type (e,e,r)

Abstract

We investigate a new lattice of generalised non-crossing partitions, constructed using the geometry of the complex reflection group $G(e,e,r)$. For the particular case $e=2$ (resp. $r=2$), our lattice coincides with the lattice of simple elements for the type $D_n$ (resp. $I_2(e)$) dual braid monoid. Using this lattice, we construct a Garside structure for the braid group $B(e,e,r)$. As a corollary, one may solve the word and conjugacy problems in this group.

38 pages, 15 figures; second version with extended introduction

References in corpus (2)

• Enumerative properties of generalized associahedra
• Garside structure for the braid group of G(e,e,r)

Cited by in corpus (5)

• Braid groups of imprimitive complex reflection groups
• A new Garside structure for braid groups of type $(e,e,r)$
• Orbites d'Hurwitz des factorisations primitives d'un élément de Coxeter
• EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
• Periodic elements in Garside groups