manuscripta mathematica

, Volume 93, Issue 1, pp 499–513

On outer automorphism groups of coxeter groups

  • R. B. Howlett
  • P. J. Rowley
  • D. E. Taylor


It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ1 andΠ2 any two bases of the root system ofW, thenΠ2 = ±ωΠ1 for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett.


Coxeter group Automorphism group Outer automorphism 


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • R. B. Howlett
    • 1
  • P. J. Rowley
    • 2
  • D. E. Taylor
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneyAustralia
  2. 2.Department of MathematicsUniversity of Manchester Institute of Science and TechnologyManchesterUnited Kingdom

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