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

RESUMO

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.