TY - JOUR
T1 - Equivariant multiplicities of Coxeter arrangements and invariant bases
AU - Abe, Takuro
AU - Terao, Hiroaki
AU - Wakamiko, Atsushi
N1 - Funding Information:
The first author was supported by JSPS Grants-in-Aid for Young Scientists (B) No. 21740014 . The second author was supported by JSPS Grants-in-Aid, Scientific Research (B) No. 21340001 .
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
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U2 - 10.1016/j.aim.2012.04.015
DO - 10.1016/j.aim.2012.04.015
M3 - Article
AN - SCOPUS:84861111146
SN - 0001-8708
VL - 230
SP - 2364
EP - 2377
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 4-6
ER -