**Abstract**
A still in general unsolved problem in exact diagonalisation studies of systems of multiple SU(n) spins transforming according to some representaiton of SU(n) is using a basis adapted to the lattice symmetries as well as well total spin. Lattice symmetries are easiest to describe in the 'S_z' basis, while total spin representations can be described using the elegant Young tableaux formalism. Inspired by a description of the eigenstates of the exactly solvable Haldane-Shastry model, we found an extension to the Young tableaux formalism which can incorporate linear momentum. This formalism works for all symmetric representations of SU(n) and allows to easily find the number of momentum eigenstates to each total spin value.