Polynomial relations among characters coming from quantum affine algebras

The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of g(n)(l). Earlier work of Kirillov and Resh etikhin proposed a generalization of these identities to the other classica l Lie algebras, and conjectured that the characters of certain finite-dimen sional representations of U-q((g) over cap) satisfy it. Here we use a posit ivity argument to show that the generalized identities have only one soluti on.