Symmetric Functions and Representations of Quantum Affine Algebras

Details Symmetric Functions and Representations of Quantum Affine Algebras Symmetric Functions and Representations of Quantum Affine Algebras

2000-11-21

arxiv.org/abs/math/0011161v1

Mathematics

Quantum Algebra

19 pages. Proceedings of "Infinite dimensional Lie theory and conformal field theory", Charlottesville, May 2000

Scientific paper

We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie algebras. One is defined via combinatorial properties and is easy to calculate; the other is closely related to the $q=1$ limit of the ``minimal affinization'' representations of quantum affine algebras. We conjecture that the two families are identical, and present supporting evidence and examples. In the special case of a highest weight that is a multiple of a fundamental weight, this reduces to a conjecture of Kirillov and Reshetikhin, recently proved by the first author.

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