Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k

Abstract

Using a form factor approach, we define and compute the character of the fusion product of rectangular representations of \hat{su}(r+1). This character decomposes into a sum of characters of irreducible representations, but with q-dependent coefficients. We identify these coefficients as (generalized) Kostka polynomials. Using this result, we obtain a formula for the characters of arbitrary integrable highest-weight representations of \hat{su}(r+1) in terms of the fermionic characters of the rectangular highest weight representations.