The Shi arrangements and the Bernoulli polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Dec 2011Embargo end date: 01 Jan 2011 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 44, pages 563-570 (issn: 0024-6093,

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Authors: Suyama, Daisuke; Terao, Hiroaki;

doi: 10.1112/blms/bdr118 , 10.48550/arxiv.1103.3214

arXiv: 1103.3214

The Shi arrangements and the Bernoulli polynomials

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Abstract

The braid arrangement is the Coxeter arrangement of the type $A_\ell$. The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we give an explicit basis construction for the derivation module of the cone over the Shi arrangement. The essential ingredient of our recipe is the Bernoulli polynomials.

We fixed a typo

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Keywords

32S22, 20F55, 11B68, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory

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