(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian
In 2002, Terao showed that every reection multi-arrangement of a real
reection group with constant multiplicity is free by providing a basis of the module
of derivations. We rst generalize Terao's result to multi-arrangements stemming from
well-generated unitary reection groups, where the multiplicity of a hyperplane depends
on the order of its stabilizer. Here the exponents depend on the exponents of the
dual reection representation. We then extend our results further to all imprimitive
irreducible unitary reection groups. In this case the exponents turn out to depend on
the exponents of a certain Galois twist of the dual reection representation that comes
from a Beynon-Lusztig type semi-palindromicity of the fake degrees.
