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Canonical Systems of Basic Invariants for Unitary Reflection Groups

Published online by Cambridge University Press:  20 November 2018

Norihiro Nakashima
Affiliation:
School of Information Environment, Tokyo Denki University, Inzai, 270-1382, Japan e-mail: nakashima@mail.dendai.ac.jp
Hiroaki Terao
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan e-mail: hterao00@za3.so-net.ne.jp e-mail: tsujie@math.sci.hokudai.ac.jp
Shuhei Tsujie
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan e-mail: hterao00@za3.so-net.ne.jp e-mail: tsujie@math.sci.hokudai.ac.jp
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Abstract

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It is known that there exists a canonical system for every finite real reflection group. In a previous paper, the first and the third authors obtained an explicit formula for a canonical system. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2016

References

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