Non-crossing partitions of type (e,e,r)
David Bessis, Ruth Corran
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 Dn (resp. I2(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.
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