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Title: A new skein theory for One-Way Yang-Baxter planar algebras

Abstract: In this talk we will introduce One-Way Yang-Baxter subfactor planar algebras which is a continuation of the classification program of subfactor planar algebras via skein theory started by Bisch and Jones. We will focus on discussing the subgroup subfactor S3 × S2 ⊂ S5 which is naturally related to Petersen graph and the rank 3 permutation group. We showed that this planar algebra is generated by its 2-box space and provide a new skein theory for this planar algebra. Moreover, we will show that each member of the family of subfactors {Sn × S2 ⊂ Sn+2 : n ≥ 3} is also generated by its 2-box space and satisfies the similar type of skein theory in a uniform way.