The Gram matrix of a Temperley-Lieb algebra is similar to the matrix of chromatic joins

TL;DR

This paper demonstrates that the matrix of chromatic joins and the Gram matrix of the Temperley-Lieb algebra are similar after rescaling, with a basis change given by diagonal matrices, revealing a structural connection.

Contribution

It establishes a similarity relation between the chromatic joins matrix and the Temperley-Lieb Gram matrix through a specific basis transformation.

Findings

Matrices are similar after rescaling

Change of basis is given by diagonal matrices

Reveals structural connection between two algebraic objects

Abstract

In this paper we show that the matrix of chromatic joins and the Gram matrix of the Temperley-Lieb algebra are similar (after rescaling), with the change of basis given by diagonal matrices.