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The double coxeter arrangement

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Title: The double coxeter arrangement
Authors: Solomon, L. Browse this author
Terao, H. Browse this author
Issue Date: 1-Apr-1997
Publisher: Department of Mathematics, Hokkaido University
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 375
Start Page: 1
End Page: 21
Abstract: Let V be Euclidean space. Let WC GL(V) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H E A choose O'.H E V* such that H = ker( O'.H ). The arrangement A is known to be free: the derivation module D(A) = {8 E Ders I 8(aH) E SaH} is a free S-module with generators of degrees equal to the exponents of W. In this paper we prove an analogous theorem for the submodule E(A) of D(A) defined by E(A) = {8 E Ders I 8(aH) E Sa.1:,-}. The degrees of the basis elements are all equal to the Coxeter number. The module E(A) may be considered a deformation of the derivation module for the Shi arrangement, which is conjectured to be free. The proof is by explicit construction using a derivation introduced by K. Saito in his theory of flat generators.
Type: bulletin (article)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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