A basis construction for the Shi arrangement of the type B_ℓ or C_ℓ

2012/05/29 by Daisuke Suyama, Suyama, Daisuke
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1205.6294

15 pages

arxiv created 2012/05/29 · arxiv updated 2012/05/30

Abstract

The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the Weyl arrangement and their parallel translations. It was introduced by J.-Y. Shi in the study of the Kazhdan-Lusztig representation of the affine Weyl groups. M. Yoshinaga showed that the cone over every Shi arrangement is free. In this paper, we construct an explicit basis for the derivation module of the cone over the Shi arrangements of the type B_ℓ or C_ℓ.

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