Robert Donley (CUNY)
Abstract
Historically, the subject of Clebsch-Gordan coefficients has been of interest in representation theory and quantum mechanics. Closed formulas for such coefficients were first given by Wigner in the theory of angular momentum. We give a third approach based on combinatorial models. Here the central objects are rectangular grids realized as Peck posets, and the associated parameter space is the semigroup of semi-magic squares of size three. We give a methodology for studying the latter space as a finite graded poset. In turn, we derive the 72 Regge symmetries for un-normalized Clebsch-Gordan coefficients using lattice path counting.