Geodesic
Splints of root systems for special Lie subalgebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 127-138

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We consider special embeddings of a Lie subalgebra into simple Lie algebras. We classify the projections of algebra root systems and obtain the conditions under which a splint appears and the branching coefficients coincide with the weight multiplicities. Although such a coincidence is infrequent, it turns out to be connected with the Gelfand–Tsetlin basis.
Keywords: Lie algebra, special subalgebra, branching, weight multiplicity, splint. 
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     author = {V. D. Lyakhovsky and A.A. Nazarov and P. I. Kakin},
     title = {Splints of root systems for special {Lie} subalgebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {185},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a11/}
}
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V. D. Lyakhovsky; A.A. Nazarov; P. I. Kakin. Splints of root systems for special Lie subalgebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 127-138. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a11/