Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. (Russian) Zbl 0637.16007

Kirillov, A. N.; Reshetikhin, N. Yu.

Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 160, 211-221 (1987).

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

MSC:

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

Keywords:

quantum integrable systems; non-co-commutative Hopf algebras; Yangian; simple Lie algebra; representations