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