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Citation: Doty, Stephen, and Anthony Giaquinto. "Origins of the Temperley-Lieb algebra: early history." arXiv preprint arXiv:2307.11929 (2023).
Tags: Expository, Pedagogical, Mathematical
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.