This article is cited in 2 papers

Splints of root systems for special Lie subalgebras

V. D. Lyakhovsky, A.A. Nazarov, P. I. Kakin

St. Petersburg State University, St. Petersburg, Russia

Abstract: 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.

DOI: 10.4213/tmf8924

 English version: Theoretical and Mathematical Physics, 2015, 185:1, 1471–1480

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