Yang-Baxter relation planar algebras

Zhengwei Liu Harvard University, Cambridge, MA 02138

Mathematical Physics Quantum Algebra Spectral Theory and Operator Algebra mathscidoc:2207.22007

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.
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  title={Yang-Baxter relation planar algebras},
  author={Zhengwei Liu},
Zhengwei Liu. Yang-Baxter relation planar algebras. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707160722363828578.
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