Emmy-Noether-Seminar

The generatingfunctionology of Clebsch-Gordan coefficients

Robert Donley (New York)

Abstract: In particle physics, Clebsch-Gordan coefficients play a central role in the theory of angular momentum, where they represent probabilities for coupled systems. By switching from orthonormal bases to ones better suited to representation theory, one obtains a theory over the integers with a strong combinatorial nature. New features include hexagonal difference tables, Catalan numbers, and a partition on the set of 3×3 semi-magic squares.