Polynomial Relations Among Characters coming from Quantum Affine Algebras

Abstract

The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of $g{l}_n$. 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.

14 pages; primarily one chapter out of math.QA/9809087

References in corpus (1)

• Pfaffian and Determinant Solutions to A Discretized Toda Equation for $B_r,C_r$ and $D_r$