An N-independent tensor decomposition for SU(N)

Stefan Keppeler, Malin Sjödahl and Bernanda Telalovic

$an equation from the paper: decomposition of a tensor product in terms of Young diagram pairs$

Abstract

To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an N-independent reduction of SU(N) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-N decomposition.