Berenstein-Zelevinsky triangles, elementary couplings and fusion rules
L. Begin, Anatol N. Kirillov, P. Mathieu, M. A. Walton
TL;DR
This paper introduces a scheme using Berenstein-Zelevinsky triangles to describe su(N)_k fusion rules, providing explicit calculations and solutions, notably for su(4)_k, enhancing understanding of algebraic structures in mathematical physics.
Contribution
The paper develops a general method to compute su(N)_k fusion rules via elementary couplings and Berenstein-Zelevinsky triangles, including a closed-form expression for threshold levels.
Findings
Closed expression for threshold levels in fusion rules
Complete solution for su(4)_k fusion rules
Explicit calculation method for elementary couplings
Abstract
We present a general scheme for describing 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 su(4)_k fusion rules is obtained.
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