Equivariant multiplicities of Coxeter arrangements and invariant bases

• Abe, Takuro

• Terao, Hiroaki

• Wakamiko, Atsushi

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

• Advances in Mathematics

  Advances in Mathematics 230 (4-6), 2364-2377, 2012-07

  Elsevier

キーワード

• Arrangement of hyperplanes
• Coxeter arrangements
• Equivariant multiplicities
• Invariant bases

詳細情報

• CRID: 1050001339010831360
• NII論文ID: 120005946712
• HANDLE: 2115/49577
• ISSN: 00018708
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles