Some Almost Exceptional Arrangements

AbstractWe introduce and study a family of real hyperplane arrangements that includes the reflection arrangements of types A and D as well as an infinite family of arrangements E′n (constructed by Orlik, Solomon, and Terao) related to the exceptional arrangements of type En, n ≤ 8. We investigate freeness (in the sense of Terao) of these arrangements, disproving the conjecture that the arrangements E′n are free in general