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

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

2005-06-28

arxiv.org/abs/math-ph/0506071v2

J. Phys. A38, 9183-9205 (2005)

Physics

Mathematical Physics

21 pages; minor changes, typos corrected

Scientific paper

10.1088/0305-4470/38/42/002

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.

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