3 research outputs found
EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
In this article we prove that the lattice of noncrossing partitions is
EL-shellable when associated with the well-generated complex reflection group
of type , for , or with the exceptional well-generated
complex reflection groups which are no real reflection groups. This result was
previously established for the real reflection groups and it can be extended to
the well-generated complex reflection group of type , for , as well as to three exceptional groups, namely and
, using a braid group argument. We thus conclude that the lattice of
noncrossing partitions of any well-generated complex reflection group is
EL-shellable. Using this result and a construction by Armstrong and Thomas, we
conclude further that the poset of -divisible noncrossing partitions is
EL-shellable for every well-generated complex reflection group. Finally, we
derive results on the M\"obius function of these posets previously conjectured
by Armstrong, Krattenthaler and Tomie.Comment: 37 pages, 4 figures. Moved the technical details of the proof of the
EL-shellability of to the appendix. More references adde