From orbital measures to Littlewood-Richardson coefficients and hive polytopes


Several combinatorial models (pictographs) can be used to determine the multiplicities (Littlewood - Richardson coefficients) of those irreducible representations (irreps) that occur in the reduction of a product of two irreps of the Lie group SU(n). Such pictographs can be considered as the integer points of an associated polytope whose volume can be expressed in terms of the Fourier transform of a convolution product of orbital measures. After describing several variants of this construction, we discuss a few properties of the volume function, whose definition makes sense in a wider context.


  • Professor Robert Coquereaux
    Professor Robert Coquereaux, CNRS, Marseille