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Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. (Russian) Zbl 0637.16007
The quantum integrable systems to which the inverse problem method can be applied are in 1-1 correspondence with representations of non-commutative and non-co-commutative Hopf algebras. Such an algebra, called a Yangian, can be constructed for any simple Lie algebra. The representation theory of Yangians also gives new results about representations of the corresponding Lie algebras.
Reviewer: L.Vaserstein

16T20 Ring-theoretic aspects of quantum groups
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
Full Text: EuDML