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Formulas for multiplicities of occurrence of irreducible components into the tensor product of representations of simple Lie algebras. (Russian. English summary) Zbl 0815.17007

L. D. Faddeev and L. A. Takhtadzhyan have shown that the formulas which were obtained by H. Bethe [Z. Phys. 71, 205-206 (1951)] indicate multiplicity of weights in the tensor product of fundamental representations of \(su(2)\). The authors deal with representations of special type of arbitrary simple Lie algebras and obtain new combinatorial formulas for multiplicities of irreducible components of tensor products of such representations. A connection of these constructions with the representation theory of Yangians is established.

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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