PreprintarXiv licencearXiv
On the extended Shi arrangement of type Bℓ
Abstract
Motivated by Kawanoue's construction of a basis for the derivation module of the cone of the extended Catalan arrangement of type Bℓ, we construct an explicit basis for the derivation module of cShi(Bℓ,m). Our construction generalizes the previously known case m=1 to m≥1. It also provides a partial answer to a question of Abe and Terao concerning explicit constructions of simple-root bases.
Related
- An explicit basis for the extended Catalan arrangement of type Dl
- A new arrangement inequality (revised and extended version)
- The generic splitting type of the logarithmic bundle of an arrangement of at most sixteen lines is combinatorial
- Laurent coefficients of Zagier-type zeta function {à} la Ishibashi and arithmetic aspects of extended Ramanujan period function
- Log-concavity of flat arrangement polynomials
BibTeX
@misc{wang2026extended,
title = {{On the extended Shi arrangement of type $B_\ell$}},
author = {Zixuan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17370},
eprint = {2609.17370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17370},
}
RIS
TY - UNPB
TI - On the extended Shi arrangement of type B_ℓ
AU - Zixuan Wang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17370
UR - https://arxiv.org/abs/2609.17370
AB - Motivated by Kawanoue's construction of a basis for the derivation module of the cone of the extended Catalan arrangement of type B_ℓ, we construct an explicit basis for the derivation module of cShi(B_ℓ,m). Our construction generalizes the previously known case m=1 to m≥1. It also provides a partial answer to a question of Abe and Terao concerning explicit constructions of simple-root bases.
ER -