Freeness of Multi-Reflection Arrangements via Primitive Vector Fields

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Date
2017-04-20MFO Scientific Program
Research in Pairs 2017Series
Oberwolfach Preprints;2017,10Author
Hoge, Torsten
Mano, Toshiyuki
Röhrle, Gerhard
Stump, Christian
Metadata
Show full item recordOWP-2017-10
Abstract
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well-generated unitary reflection groups, where the multiplicity of a hyperplane depends on the order of its stabilize. Here the exponents depend on the exponents of the dual reflection representation. When then extend our results further to all imprimitive irreducible unitary reflection groups. In this case the exponents turn out to depend on the exponents of a certain Galois twist of the dual reflection representation that comes from a Beynon-Lusztig type semi-palindromicity of fake degrees.