Yang-Baxter relation planar algebras Article Swipe

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Zhengwei Liu ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1507.06030 · OA: W2206241616

We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic construction of a new parameterized planar algebra. We construct infinitely many new subfactors and unitary fusion categories, and compute their trace formula as a closed-form expression, in terms of Young diagrams.