Explicit description of a basis for derivations of a Coxeter multiarrangement of type B₂

2023/12/11 by Shota Maehara, Maehara, Shota, Yasuhide Numata +1
Computer Science · Mathematics · #32S22 #52C35 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2312.06356

openalex publication_date 2023/12/11 · openalex created_date 2023/12/14 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the multiarrangements whose underlying arrangements are the Coxeter arrangement of type B₂. For some special multiplicities, we give an explicit description of bases for the derivation modules. As an application, we also describe the lower derivations of bases for the derivation modules of some Coxeter multiarrangements of type A₂, which are different from ones given by Wakamiko.

Related

• Coxeter multiarrangements with quasi-constant multiplicities
• A basis construction of the extended Catalan and Shi arrangements of the type A₂
• The primitive derivation and freeness of multi-Coxeter arrangements
• A generalized logarithmic module and duality of Coxeter multiarrangements
• Extendability of the B₂-arrangement