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

  title={Non-crossing partitions of type ( e , e , r )},
  author={David Bessisa and Ruth Corranb},
  • David Bessisa, Ruth Corranb
  • Published 2006
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. © 2005 Elsevier Inc. All rights reserved. 
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