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Hokkaido University Preprint Series in Mathematics >
The double coxeter arrangement
| 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) |
| URI: | http://hdl.handle.net/2115/69125 |
| 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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Submitter: 数学紀要登録作業用
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