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

David Bessis·Ruth Corran
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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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David Bessis, Ruth Corran. 2004-04-21. Non-crossing partitions of type (e,e,r). https://arxiv.org/abs/math/0403400

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