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Equivariant multiplicities of Coxeter arrangements and invariant bases

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Title: Equivariant multiplicities of Coxeter arrangements and invariant bases
Authors: Abe, Takuro Browse this author
Terao, Hiroaki Browse this author →KAKEN DB
Wakamiko, Atsushi Browse this author
Keywords: Arrangement of hyperplanes
Coxeter arrangements
Equivariant multiplicities
Invariant bases
Issue Date: Jul-2012
Publisher: Elsevier
Journal Title: Advances in Mathematics
Volume: 230
Issue: 4-6
Start Page: 2364
End Page: 2377
Publisher DOI: 10.1016/j.aim.2012.04.015
Abstract: Let A be an irreducible Coxeter arrangement and W be its Coxeter group. Then W naturally acts on A. A multiplicity m : A → Z is said to be equivariant when m is constant on each W-orbit of A. In this article, we prove that the multi-derivation module D(A, m) is a free module whenever m is equivariant by explicitly constructing a basis, which generalizes the main theorem of [T2002]. The main tool is a primitive derivation and its covariant derivative. Moreover, we show that the W-invariant part D(A, m)W for any multiplicity m is a free module over the W-invariant subring.
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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