Diagrammatic group theory in quark models

A simple and systematic diagrammatic method is presented for calculating the numerical factors arising from group theory in quark models: dimensions, casimir invariants, vector coupling coefficients, and especially recoupling coefficients. Some coefficients for the coupling of three-quark objects are listed for $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ and $\mathrm{SU}\mathrm{}\left(2n\right)\mathrm{}$.