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be a complex reflection group and
the set of the mirrors of the complex reflections in
. It is known that the complement
of the reflection arrangement
an intersection of hyperplanes in
be the complement in
of the hyperplanes in
. We hope that
is always a
. We prove it in case of the monomial groups
. Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this
property remains to be proved.
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