Nakashima, Norihiro - Bases for modules of differential operators

dmtcs:3047 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Bases for modules of differential operators

Authors: Nakashima, Norihiro

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''.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Coxeter arrangement, Cauchy―Sylvester's compound determinants, Schur functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]