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arXiv · 1712.04878

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

Cristina Ana-Maria Anghel
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Abstract

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.

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BibTeXRIS

Cristina Ana-Maria Anghel. 2017-12-13. A combinatorial description of the centralizer algebras connected to the Links-Gould Invariant. https://doi.org/10.2140/agt.2021.21.1553

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