Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type $B_{\ell }$

Abstract

Every subarrangement of Weyl arrangements of type $B_{\ell }$ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $A_{\ell -1}$ and type $B_{\ell }$ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $B_{\ell }$ in terms of graphs.

15 pages