Ziegler’s Multireflection Arrangements Are Free

Abstract

In 1989, Ziegler introduced the concept of a multiarrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all but three irreducible groups, Ziegler showed that each such multireflection arrangement is free. We complete Ziegler’s example by confirming these outstanding cases.

Keywords::

• multiarrangement
• reflection arrangement
• free arrangement
• complex reflection group
• 20F55
• 52C35
• 14N20