On outer automorphism groups of coxeter groups |
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| Authors: | R B Howlett P J Rowley D E Taylor |
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| Institution: | (1) School of Mathematics and Statistics, University of Sydney, 2006, NSW, Australia;(2) Department of Mathematics, University of Manchester Institute of Science and Technology, M60 1QD Manchester, United Kingdom |
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| Abstract: | Summary 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 andΠ
1 andΠ
2 any two bases of the root system ofW, thenΠ
2 = ±ωΠ
1 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.
This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991. |
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| Keywords: | Coxeter group Automorphism group Outer automorphism |
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