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

TL;DR

This paper introduces a method to compute characters of fusion products of rectangular representations in affine su(r+1), expressing them through Kostka polynomials and deriving formulas for general highest-weight representations.

Contribution

It defines and computes fusion product characters using a form factor approach, linking them to Kostka polynomials and providing new formulas for arbitrary integrable representations.

Findings

Fusion product characters decompose into irreducible characters with q-dependent Kostka polynomial coefficients.

Derived a formula expressing arbitrary highest-weight characters in terms of rectangular representation fermionic characters.

Established a connection between fusion products, Kostka polynomials, and fermionic characters in affine su(r+1).

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.