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A note on sums of roots. (English) Zbl 1431.17007

Summary: In this paper, we look at properties of roots which can be written as sums of roots in crystallographic root systems. We derive properties of the poset associated to such a sum consisting of the subsums which are themselves roots.

MSC:

17B22 Root systems
20F55 Reflection and Coxeter groups (group-theoretic aspects)

Software:

POSETS
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References:

[1] N. Bourbaki, Lie groups and Lie algebras, Springer-Verlag, Berlin, 2008. · Zbl 1145.17002
[2] B.A. Davey and H.A. Priestley, Introduction to lattices and order, Cambridge University Press, Cambridge, 2002. · Zbl 1002.06001
[3] M.J. Dyer and G.I. Lehrer, Parabolic subgroup orbits on finite root systems, J. Pure Appl. Alg., to appear. · Zbl 1398.20048
[4] C. Greene, POSETS package, http://ww3.haverford.edu/math/cgreene/posets.html.
[5] R. Stanley, Enumerative combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.
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