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On Closed Subsets of Root Systems

Published online by Cambridge University Press:  20 November 2018

D. Ž. Doković ,
P. Check  and
J.-Y. Hée
D. Ž. Doković
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1
P. Check
Affiliation:
Department of Mathematics University of Michigan Ann Arbor, Michigan 48109-1003 U.S.A.
J.-Y. Hée
Affiliation:
Université Paris-Sud Mathématique, Bât. 425 91405 Orsay, Cedex France
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Abstract

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Let R be a root system (in the sense of Bourbaki) in a finite dimensional real inner product space V. A subset P ⊂ R is closed if α, β ∊ P and α + β ∊ R imply that α + β ∊ P. In this paper we shall classify, up to conjugacy by the Weyl group W of R, all closed sets P ⊂ R such that R\P is also closed. We also show that if θ:R —> R′ is a bijection between two root systems such that both θ and θ-1 preserve closed sets, and if R has at most one irreducible component of type A1, then θ is an isomorphism of root systems.

Keywords

17B67
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 338 - 345
Copyright
Copyright © Canadian Mathematical Society 1994

References

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