Geodesic
On Compositions Associated to Frobenius Parabolic and Seaweed Subalgebras of sln(k)
Journal of Lie theory, Tome 25 (2015) no. 4, pp. 1191-1213
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By using a free monoid of operators on the set of compositions (respectively, pairs of compositions), we establish in this paper a bijective correspondence between Frobenius standard parabolic (respectively, seaweed) subalgebras and certain elements of this monoid. We prove via this correspondence a conjecture of one of the authors on the number of Frobenius standard parabolic (respectively, seaweed) subalgebras of sln(k) associated to compositions (respectively, pairs of compositions) with n-t parts (respectively, parts in total).
Classification : 17B08, 05A16
Mots-clés : Frobenius parabolic and seaweed Lie algebras 
@article{JLT_2015_25_4_JLT_2015_25_4_a11,
     author = {M. Duflo and R. W. T. Yu},
     title = {On {Compositions} {Associated} to {Frobenius} {Parabolic} and {Seaweed} {Subalgebras} of sl\protect\textsubscript{n}(k)},
     journal = {Journal of Lie theory},
     pages = {1191--1213},
     year = {2015},
     volume = {25},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a11/}
}
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M. Duflo; R. W. T. Yu. On Compositions Associated to Frobenius Parabolic and Seaweed Subalgebras of sln(k). Journal of Lie theory, Tome 25 (2015) no. 4, pp. 1191-1213. http://geodesic.mathdoc.fr/item/JLT_2015_25_4_JLT_2015_25_4_a11/