Fusion products

doi:10.1088/0305-4470/38/42/002

Fusion products, Kostka polynomials and fermionic characters of $\widehat{su}(r+1)_k$

Eddy Ardonne et al 2005 J. Phys. A: Math. Gen. 38 9183-9205 doi: 10.1088/0305-4470/38/42/002

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Eddy Ardonne¹, Rinat Kedem² and Michael Stone¹
¹ Department of Physics, University of Illinois, 1110 W Green St., Urbana, IL 61801, USA
² Department of Mathematics, University of Illinois, 1409 W Green St., Urbana, IL 61801, USA

Abstract. Using a form factor approach, we define and compute the character of the fusion product of rectangular representations of $\widehat{su}(r+1)$ . 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 $\widehat{su}(r+1)$ in terms of the fermionic characters of the rectangular highest weight representations.

PACS numbers: 03.65.Fd, 02.20.Tw, 11.25.Hf

Print publication: Issue 42 (21 October 2005)
Received 3 July 2005, in final form 26 August 2005
Published 5 October 2005

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Fusion products, Kostka polynomials and fermionic characters of $\widehat{su}(r+1)_k$

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