From tensor category to Temperley-Lieb algebra representation

Abstract

We construct a representation of the Temperley-Lieb algebra from a multiplicity-free semisimple monoidal Abelian category $\mathcal{C}$, with two simple objects $\lambda$ and $\nu$ such that $\lambda \otimes \nu$ is simple and Hom${}_{\mathcal{C}}(\lambda \otimes \lambda ,\nu )$ is not empty. A self-contained manual to tensor categories is also provided as well as a summary of the best known example of the construction: Schur-Weyl duality for $U_q(s{l}_2))$.

20 pages, 19 figures

References in corpus (1)

• Interacting anyons in topological quantum liquids: The golden chain

Cited by in corpus (1)

• Temperley-Lieb and Birman-Murakami-Wenzl like relations from multiplicity free semi-simple tensor system