From orbital measures to Littlewood-Richardons coefficients and hive polytopes

Expositor: Robert Coquereaux
17/10/2017 , 15:30 | Sala 236.

The volume of the hive polytope  (or polytope of honeycombs) associated with a Littlewood-Richardson coefficient of SU(n), or with a given admissible triple of highest weights, can be expressed, in the generic case, in terms  of the Fourier transform of a convolution product of orbital measures. This volume can be thought of as a semi-classical approximation of Littlewood-Richardson coefficients and it is related to the stretching polynomials or to the Ehrhart polynomials of the relevant hive polytopes. In this talk, based on a joined work with J.-B. Zuber, we shall recall what are the Knutson-Tao honeycombs, describe other variants of these pictographs, and illustrate the above properties on several SU(n) examples for n=2,3,..,6.