Hokkaido Mathematical Journal

Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations

Atsushi WAKAMIKO

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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.

Article information

Source
Hokkaido Math. J., Volume 40, Number 3 (2011), 375-392.

Dates
First available in Project Euclid: 26 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1319595862

Digital Object Identifier
doi:10.14492/hokmj/1319595862

Mathematical Reviews number (MathSciNet)
MR2883497

Zentralblatt MATH identifier
1233.32020

Subjects
Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35]

Keywords
Coxeter arrangement Coxeter group multi-arrangement primitive derivation multi-derivation module logarithmic differential form

Citation

WAKAMIKO, Atsushi. Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations. Hokkaido Math. J. 40 (2011), no. 3, 375--392. doi:10.14492/hokmj/1319595862. https://projecteuclid.org/euclid.hokmj/1319595862


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