Equivariant multiplicities of Coxeter arrangements and invariant bases
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.
収録刊行物
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- Advances in Mathematics
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Advances in Mathematics 230 (4-6), 2364-2377, 2012-07
Elsevier
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詳細情報 詳細情報について
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- CRID
- 1050001339010831360
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- NII論文ID
- 120005946712
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- HANDLE
- 2115/49577
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- ISSN
- 00018708
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- IRDB
- CiNii Articles