The generator conjecture for 3^G subfactor planar algebras

2015/07/16 by Liu, Zhengwei, Penneys, David
#18D10 #46L37 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1507.04794

Abstract

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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