Fusion products, Kostka polynomials and fermionic characters of su-hat(r+1)k

Using a form factor approach, we define and compute the character of the fusion product of rectangular representations of su-hat(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 su-hat(r+1) in terms of the fermionic characters of the rectangular highest weight representations