A type $B$ analog of Ish arrangement

Abstract

The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type $A$ Coxeter arrangement that share many common properties. Motivated by a question of Armstrong and Rhoades since 2012 to seek for Ish arrangements of other types, in this paper we introduce an Ish arrangement of type $B$. We study this Ish arrangement through various aspects similar to as known in type $A$ with a main emphasis on freeness and supersolvability. Our method is based on the concept of $\psi$-digraphic arrangements recently introduced due to Abe and the authors with a type $B$ extension.