Journal of Lie Theory 25 (2015), No. 4, 1191--1213
Copyright Heldermann Verlag 2015
On Compositions Associated to Frobenius Parabolic and Seaweed Subalgebras of sln(k)
Michel Duflo
UFR de Mathématiques, Université Paris Diderot, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France
michel.duflo@imj-prg.fr
Rupert W. T. Yu
Laboratoire de Mathématiques, U.F.R. Sciences Exactes et Naturelles, Université de Reims, Moulin de la Housse - BP 1039, 51687 Reims Cedex 2, France
rupert.yu@univ-reims.fr
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).
Keywords: Frobenius parabolic and seaweed Lie algebras.
MSC: 17B08, 05A16
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