A combinatorial description of the centralizer algebras connected to the Links–Gould invariant

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