2024-03-29T12:20:54Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/495772022-11-17T02:08:08Zhdl_2115_20039hdl_2115_116Equivariant multiplicities of Coxeter arrangements and invariant basesAbe, Takuro1000090119058Terao, HiroakiWakamiko, Atsushiopen accessArrangement of hyperplanesCoxeter arrangementsEquivariant multiplicitiesInvariant bases411Let 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.Elsevier2012-07engjournal articleAMhttp://hdl.handle.net/2115/49577https://doi.org/10.1016/j.aim.2012.04.0150001-8708Advances in Mathematics2304-623642377https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/49577/1/AiM230-4-6_2364-2377.pdfapplication/pdf126.29 KB2012-07