Fusion Products, Kostka Polynomials and Fermionic Characters of

Abstract

Using a form factor approach, we define and compute the character of the fusion product of rectangular representations of ŝu(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 ŝu(r + 1) in terms of the fermionic characters of the rectangular highest weight representations. PACS numbers: 03.65.Fd, 02.20.Tw, 11.25.Hf 1