Equivariant multiplicities of Coxeter arrangements and invariant bases

Abe, Takuro; Terao, Hiroaki; Wakamiko, Atsushi

Advances in Mathematics, 2012, 230(4-6), 2364-2377

Permalink : https://hdl.handle.net/2115/49577

このアイテムのアクセス数:941件（2026-10-07 21:04 集計）

ファイル	フォーマット	サイズ	閲覧回数	説明
AiM230-4-6_2364-2377	pdf	126 KB	798

アクセス権	open access
URI	https://hdl.handle.net/2115/49577
タイトル	Equivariant multiplicities of Coxeter arrangements and invariant bases
著者	Abe, Takuro ; Terao, Hiroaki ; Wakamiko, Atsushi
著者名 Abe, Takuro
e-Rad_Researcher 90119058 著者名 Terao, Hiroaki
著者名 Wakamiko, Atsushi
言語	英語
キーワード	Arrangement of hyperplanes
	Coxeter arrangements
	Equivariant multiplicities
	Invariant bases
発行日	2012-07
出版者	Elsevier
収録物名	Advances in Mathematics
巻(号)	230(4-6)
ページ	2364-2377
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
PISSN	0001-8708
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1016/j.aim.2012.04.015