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Simple-root bases for Shi arrangements

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Title: Simple-root bases for Shi arrangements
Authors: Abe, Takuro Browse this author
Terao, Hiroaki Browse this author →KAKEN DB
Keywords: Arrangements of hyperplanes
Weyl arrangements
Free arrangements
Shi arrangements
Root systems
Issue Date: 15-Jan-2015
Publisher: Elsevier
Journal Title: Journal of algebra
Volume: 422
Start Page: 89
End Page: 104
Publisher DOI: 10.1016/j.jalgebra.2014.09.011
Abstract: In his affirmative answer to the Edelman-Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, we know very little about the bases themselves except their existence. In this article, we prove the unique existence of two distinguished bases which we call the simple-root basis plus (SRB+) and the simple-root basis minus (SRB-). They are characterized by nice divisibility properties relative to the simple roots.
Rights: (C) 2014 Elsevier Inc. All rights reserved.
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 寺尾 宏明

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