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.
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