A type \(B\) analog of Ish arrangement

authored by

Nhat Tan Tran, Shuhei Tsujie

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Hokkaido University of Education

Type

Preprint

Publication date

24.04.2023

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2304.12022 (Access: Open)