Equivariant multiplicities of Coxeter arrangements and invariant bases

Takuro Abe, Hiroaki Terao, Atsushi Wakamiko

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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 Terao (2002). [12]. 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.

Original languageEnglish
Pages (from-to)2364-2377
Number of pages14
JournalAdvances in Mathematics
Volume230
Issue number4-6
DOIs
Publication statusPublished - Jul 1 2012
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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