Flynn, G.; Rasmussen, J.; Tahić, M.; Walton, M. A. Higher-genus \(\text{su}(N)\) fusion multiplicities as polytope volumes. (English) Zbl 1046.81515 J. Phys. A, Math. Gen. 35, No. 47, 10129-10147 (2002). Summary: We show how higher-genus \(su(N)\) fusion multiplicities may be computed as the discretized volumes of certain polytopes. The method is illustrated by explicit analyses of some \(su(3)\) and \(su(4)\) fusions, but applies to all higher-point and higher-genus \(su(N)\) fusions. It is based on an extension of the realm of Berenstein-Zelevinsky triangles by including so-called gluing and loop-gluing diagrams. The identification of the loop-gluing diagrams is our main new result, since they enable us to characterize higher-genus fusions in terms of polytopes. Also, the genus-2 0-point \(su(3)\) fusion multiplicity is found to be a simple binomial coefficient in the affine level. MSC: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 22E46 Semisimple Lie groups and their representations 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 81T99 Quantum field theory; related classical field theories PDFBibTeX XMLCite \textit{G. Flynn} et al., J. Phys. A, Math. Gen. 35, No. 47, 10129--10147 (2002; Zbl 1046.81515) Full Text: DOI arXiv