The generator conjecture for 3^G subfactor planar algebras

Zhengwei Liu David Penneys

Functional Analysis mathscidoc:2207.12002

Proceedings of the Centre for Mathematics and its Applications, Australian National University, 46, 344-366, 2017.2
We state a conjecture for the formulas of the depth 4 low-weight rotational eigenvectors and their corresponding eigenvalues for the 3^G subfactor planar algebras. We prove the conjecture in the case when |G| is odd. To do so, we find an action of G on the reduced subfactor planar algebra at f^{(2)}, which is obtained from shading the planar algebra of the even half. We also show that this reduced subfactor planar algebra is a Yang-Baxter planar algebra.
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@inproceedings{zhengwei2017the,
  title={The generator conjecture for 3^G subfactor planar algebras},
  author={Zhengwei Liu, and David Penneys},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154242619028528},
  booktitle={Proceedings of the Centre for Mathematics and its Applications, Australian National University},
  volume={46},
  pages={344-366},
  year={2017},
}
Zhengwei Liu, and David Penneys. The generator conjecture for 3^G subfactor planar algebras. 2017. Vol. 46. In Proceedings of the Centre for Mathematics and its Applications, Australian National University. pp.344-366. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154242619028528.
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