N-point and higher-genus osp(1∣2) fusion

We study affine osp(1∣2) fusion, the fusion in osp(1∣2) conformal field theory, for example. Higher-point and higher-genus fusion is discussed. The fusion multiplicities are characterized as discretized volumes of certain convex polytopes, and are written explicitly as multiple sums measuring those volumes. We extend recent methods developed to treat affine su(2) fusion. They are based on the concept of generalized Berenstein–Zelevinsky triangles and virtual couplings. Higher-point tensor products of finite-dimensional irreducible osp(1∣2) representations are also considered. The associated multiplicities are computed and written as multiple sums