An $\textit{N}$-independent tensor decomposition for SU($\textit{N}$)
Stefan Keppeler (Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, Tübingen, D-72076, Germany)
; Malin Sjodahl (Department of Physics, Lund University, Lund, SE-221 00, Sweden); Bernanda Telalovic (Institute of Physics, NAWI Graz, University of Graz, Universitätsplatz 5, Graz, A-8010, Austria, Niels Bohr International Academy, Københavns Universitet, Blegdamsvej 17, Copenhagen, DK-2100, Denmark)
To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $\textit{N}$-independent reduction of SU($\textit{N}$) 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-$\textit{N}$ decomposition.
