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Polynomial Relations Among Characters coming from Quantum Affine Algebras

Michael Kleber
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Abstract

The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of $gl_n$. Earlier work of Kirillov and Reshetikhin proposed a generalization of these identities to the other classical Lie algebras, and conjectured that the characters of certain finite-dimensional representations of $U_q(g-affine)$ satisfy it. Here we use a positivity argument to show that the generalized identities have only one solution.

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Michael Kleber. 1999-03-01. Polynomial Relations Among Characters coming from Quantum Affine Algebras. https://arxiv.org/abs/math/9903008

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