Geodesic
Abelian ideals of a Borel subalgebra and root systems
Journal of the European Mathematical Society, Tome 16 (2014) no. 12, pp. 2693-2708 Cet article a éte moissonné depuis la source EMS Press

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Let g be a simple Lie algebra and Abo the poset of non-trivial abelian ideals of a fixed Borel subalgebra of g. In [8], we constructed a partition Abo=⊔μ​Abμ​ parameterised by the long positive roots of g and studied the subposets Abμ​. In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of g is a join-semilattice.
DOI : 10.4171/jems/496
Classification : 17-XX, 00-XX, 20-XX
Keywords: Root system, Borel subalgebra, minuscule element, abelian ideal 
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     author = {Dmitri I. Panyushev},
     title = {Abelian ideals of a {Borel} subalgebra and root systems},
     journal = {Journal of the European Mathematical Society},
     pages = {2693--2708},
     year = {2014},
     volume = {16},
     number = {12},
     doi = {10.4171/jems/496},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/496/}
}
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Dmitri I. Panyushev. Abelian ideals of a Borel subalgebra and root systems. Journal of the European Mathematical Society, Tome 16 (2014) no. 12, pp. 2693-2708. doi: 10.4171/jems/496

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