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Symmetric Functions and Representations of Quantum Affine Algebras

Vyjayanthi Chari·Michael Kleber
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Abstract

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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Vyjayanthi Chari, Michael Kleber. 2000-11-21. Symmetric Functions and Representations of Quantum Affine Algebras. https://arxiv.org/abs/math/0011161

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