Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
arXiv:1405.6379 · doi:10.1007/s10801-015-0624-z
Abstract
In this article we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual-partition formula. Then it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each filter is a free subarrangement satisfying the dual-partition formula. This generalizes the main result in \cite{ABCHT} which affirmatively settled a conjecture by Sommers and Tymoczko \cite{SomTym}.