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October 2011 Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations
Atsushi WAKAMIKO
Hokkaido Math. J. 40(3): 375-392 (October 2011). DOI: 10.14492/hokmj/1319595862

Abstract

Let ¥cal{A} be an irreducible Coxeter arrangement and k be a multiplicity of ¥cal{A}. We study the derivation module D(¥cal{A}, k). Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the action of the Coxeter group. In this paper, we will explicitly construct a basis for D(¥cal{A}, k) assuming k is constant on each orbit. Consequently we will determine the exponents of (¥cal{A}, k) under this assumption. For this purpose we develop a theory of universal derivations and introduce a map to deal with our exceptional cases.

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Atsushi WAKAMIKO. "Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations." Hokkaido Math. J. 40 (3) 375 - 392, October 2011. https://doi.org/10.14492/hokmj/1319595862

Information

Published: October 2011
First available in Project Euclid: 26 October 2011

zbMATH: 1233.32020
MathSciNet: MR2883497
Digital Object Identifier: 10.14492/hokmj/1319595862

Subjects:
Primary: 32S22

Rights: Copyright © 2011 Hokkaido University, Department of Mathematics

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Vol.40 • No. 3 • October 2011
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