Splints of root systems for special Lie subalgebras. (English. Russian original) Zbl 1387.17021
Theor. Math. Phys. 185, No. 1, 1471-1480 (2015); translation from Teor. Mat. Fiz. 185, No. 1, 127-138 (2015).
Summary: 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.
MSC:
| 17B22 | Root systems |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
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