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Korff and Stroppel discovered a realization of su(n) affine fusion, thefusion of the su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theory,in the phase model, a limit of the q-boson hopping model. This integrable-modelrealization provides a new perspective on affine fusion, explored in a recentpaper by the author. The role of WZNW primary fields is played in it bynon-commutative Schur polynomials, and fusion coefficients are thus given by anon-commutative version of the Verlinde formula. We present the extension toall Verlinde dimensions, of arbitrary genus and any number N of points. Thelevel-dependence of affine fusion is also discussed, using the concept ofthreshold level, and its generalization to threshold weight.

Hopping in the Phase Model to a Non-Commutative Verlinde Formula for Affine Fusion