Abstract
We present a general scheme for describing\(\widehat{su}\)(N) k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way, a complete solution of\(\widehat{su}\)(4) k fusion rules is obtained.
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Work supported by NSERC (Canada).
Work supported by NSERC (Canada) and FCAR (Québec).
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Begin, L., Kirillov, A.N., Mathieu, P. et al. Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Lett Math Phys 28, 257–268 (1993). https://doi.org/10.1007/BF00761494
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DOI: https://doi.org/10.1007/BF00761494