The double Coxeter arrangement |
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Authors: | L Solomon H Terao |
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Institution: | (1) Mathematics Department, University of Wisconsin, Madison WI 53706, USA , US;(2) Mathematics Department, University of Wisconsin, Madison WI 53706, USA, e-mail: hterao@facstaff.wisc.edu , US |
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Abstract: | Let V be Euclidean space. Let be a finite irreducible reflection group. Let be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For choose such that . The arrangement is known to be free: the derivation module 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 of defined by . The degrees of the basis elements are all equal to the Coxeter number. The module 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.
Received: March 13, 1997 |
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Keywords: | , Hyperplane arrangement, free arrangement, Shi arrangement, reflection group, basic invariants, Coxeter number,,,,,,Jacobian matrix, |
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