Citation: Doty, Stephen, and Anthony Giaquinto. "Origins of the Temperley-Lieb algebra: early history." arXiv preprint arXiv:2307.11929 (2023).
Web: https://arxiv.org/abs/2307.11929
Tags: Expository, Pedagogical, Mathematical, Subfactors, Quantum-groups
This paper gives a lovely historically-minded introduction to Temperley-Lieb-Jones algebras, and their representations. All of the basic facts are summarized, with references, and simple proofs are given.
A very short section is devoted to the connection with quantum groups. Namely, Schur-Weyl duality between the Temperley-Lieb algebra and the quantum group of sl_2(C) is stated.
This paper and the references within it seem like a perfect place to get started for learning about Temperley-Lieb algebras.