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The Shi arrangement is an affine arrangement of hyperplanes consisting of thehyperplanes of the Weyl arrangement and their parallel translations. It wasintroduced by J.-Y. Shi in the study of the Kazhdan-Lusztig representation ofthe affine Weyl groups. M. Yoshinaga showed that the cone over every Shiarrangement is free. In this paper, we construct an explicit basis for thederivation module of the cone over the Shi arrangements of the type $B_{\ell}$or $C_{\ell}$.

A basis construction for the Shi arrangement of the type $B_{\ell}$ or $C_{\ell}$