Geodesic
On Closed Subsets of Root Systems
Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 338-345

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DOI

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 A 1, then θ is an isomorphism of root systems.
DOI : 10.4153/CMB-1994-050-4
Mots-clés : 17B67 
Doković, D. Ž.; Check, P.; Hée, J.-Y. On Closed Subsets of Root Systems. Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 338-345. doi: 10.4153/CMB-1994-050-4
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     title = {On {Closed} {Subsets} of {Root} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {338--345},
     year = {1994},
     volume = {37},
     number = {3},
     doi = {10.4153/CMB-1994-050-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-050-4/}
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