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Characters of fundamental representations of quantum affine algebras. (English) Zbl 1101.17016
In this paper the authors use inductive methods to give closed formulas for the \(q\)-characters of all the fundamental representations of the quantum loop algebras of classical simple Lie algebras. The answer is combinatorial and given in terms of some partitions satisfying certain simple properties. Some formulas for the multiplicities of the eigenvalues of the imaginary subalgebra in terms of these partitions are also obtained. The proof is rather technical and involves a case-by-case analysis of all finite-dimensional classical simple Lie algebras.

17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20G42 Quantum groups (quantized function algebras) and their representations
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