Equivariant multiplicities of Coxeter arrangements and invariant bases


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Please use this identifier to cite or link to this item:http://hdl.handle.net/2115/49577

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)
URI:	http://hdl.handle.net/2115/49577
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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