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In this paper we study the tensor powers of the standard representation ofthe quantum super-algebra $U_q(sl(2|1)$, focusing on the rings of its algebraendomorphisms, called centraliser algebras and denoted by $LG_n$. Theirdimensions were conjectured by I. Marin and E. Wagner \cite{MW}. We prove thisconjecture, describing the intertwiner spaces from a semi-simple decompositionas sets consisting of certain paths in a planar lattice with integercoordinates. Using this model, we present a matrix unit basis for thecentraliser algebra $LG_n$, by means of closed curves in the plane, which areincluded in the lattice with integer coordinates.

A combinatorial description of the centralizer algebras connected to the Links-Gould Invariant