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math.CO2011
Modules of differential operators of order 2 on Coxeter arrangements
Norihiro Nakashima
We prove that the modules of differential operators of order 2 on the classical Coxeter arrangements are free by exhibiting bases. For this purpose, we use Cauchy-Sylvester's theor…
math.CO2011
The Freeness and Minimal Free Resolutions of Modules of Differential Operators of a Generic Hyperplane Arrangement
Norihiro Nakashima, Go Okuyama, Mutsumi Saito
Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A)…
math.RA2011
The noetherian properties of the rings of differential operators on central 2-arrangements
Norihiro Nakashima
Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is sti…