A combinatorial description of the centralizer algebras connected to the Links-Gould Invariant
arXiv:1712.04878 · doi:10.2140/agt.2021.21.1553
Abstract
In this paper we study the tensor powers of the standard representation of the quantum super-algebra , focusing on the rings of its algebra endomorphisms, called centraliser algebras and denoted by . 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 , by means of closed curves in the plane, which are included in the lattice with integer coordinates.
27 pages, Added the description of a basis of matrix units for the centraliser algebra LG_n