Polynomial Relations Among Characters coming from Quantum Affine Algebras

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

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Published 1 January 1998