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- W2724671567 abstract "It is well-known that the derivation modules of Coxeter arrangements are free. Holm began to study the freeness of modules of differential operators on hyperplane arrangements. In this paper, we study the cases of the Coxter arrangements of type A, B and D. In this case, we prove that the modules of differential operators of order 2 are free. We give examples of all the 3-dimensional classical Coxeter arrangements. Two keys for the proof are ``Cauchy–Sylvester's theorem on compound determinants'' and ``Saito–Holm's criterion''. Il est connu que les modules de la dérivation d'arrangements de Coxeter sont libres. Holm a commencè à étudier les modules libres des opérateurs différentiels sur des compositions d'hyperplans. Dans cet article, nous étudions les cas des compositions de Coxter les types A, B et D. Dans ce cas, nous prouvons que les modules d’opérateurs différentiels d'ordre 2 sont libres. Nous donnons des exemples de toutes les compositions de Coxeter classiques de dimension 3. Les deux points clefs pour la preuve sont le théorème de Cauchy–Sylvester sur déterminants composés et le critère de Saito–Holm." @default.
- W2724671567 created "2017-07-14" @default.
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- W2724671567 date "2012-01-01" @default.
- W2724671567 modified "2023-09-25" @default.
- W2724671567 title "Bases for modules of differential operators" @default.
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- W2724671567 doi "https://doi.org/10.46298/dmtcs.3047" @default.
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