Yang-Baxter relation planar algebras

Abstract

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.

77 pages, 159 figures

References in corpus (2)

• Young's lattice and dihedral symmetries revisited: Möbius strips and metric geometry
• Singly generated planar algebras of small dimension, Part III

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