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arXiv · 2609.17370

On the extended Shi arrangement of type $B_{\ell}$

Zixuan Wang
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Abstract

Motivated by Kawanoue's construction of a basis for the derivation module of the cone of the extended Catalan arrangement of type $B_\ell$, we construct an explicit basis for the derivation module of $\mathbf{c}Shi(B_\ell,m)$. Our construction generalizes the previously known case $m=1$ to $m\geq1$. It also provides a partial answer to a question of Abe and Terao concerning explicit constructions of simple-root bases.

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Zixuan Wang. 2026-09-15. On the extended Shi arrangement of type $B_{\ell}$. https://arxiv.org/abs/2609.17370

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