Algebra Seminar: Coquereaux -- Honeycombs, polytopes, and orbital measures: another look at representation theory

Robert Coquereaux (Aix-Marseille Universite) 

Wednesday 13 March, 12-1pm, Place: Carslaw 375 

Title: Honeycombs, polytopes, and orbital measures: another look at representation
theory.  

Abstract: 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.