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Quantum affine algebras. (English) Zbl 0739.17004
The authors classify the finite-dimensional irreducible representations of the quantum affine algebra \(U_ q(\hat sl_ 2)\) in terms of highest weights. They also give an explicit construction of all such representations by means of an evaluation homomorphism \(U_ q(\hat sl_ 2)\to U_ q(sl_ 2)\). This is used to compute the trigonometric \(R\)- matrices associated to finite-dimensional representations of \(U_ q(\hat sl_ 2)\).

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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