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Canonical Systems of Basic Invariants for Unitary Reflection Groups

  Published:2016-06-01
 Printed: Sep 2016
  • Norihiro Nakashima,
    School of Information Environment, Tokyo Denki University, Inzai, 270-1382, Japan
  • Hiroaki Terao,
    Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan
  • Shuhei Tsujie,
    Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan
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Abstract

It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. 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.
Keywords: basic invariant, invariant theory, finite unitary reflection group basic invariant, invariant theory, finite unitary reflection group
MSC Classifications: 13A50, 20F55 show english descriptions Actions of groups on commutative rings; invariant theory [See also 14L24]
Reflection and Coxeter groups [See also 22E40, 51F15]
13A50 - Actions of groups on commutative rings; invariant theory [See also 14L24]
20F55 - Reflection and Coxeter groups [See also 22E40, 51F15]
 

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