Speaker
Yasuyuki Kawahigashi
(University of Tokyo)
Description
We study 3-tensors satisfying the "zipper condition", which play an important role in tensor network approaches to two-dimensional topological order. We identified the 4-tensors appearing in these approaches with bi-unitary connections in the Jones theory of subfactors in operator algebras before. We now prove that, when the bi-unitary connection produces a subfactor of finite depth, the 3-tensors satisfying the zipper condition correspond precisely to the quantum 6j-symbols, also known as F-symbols, of the unitary multi-fusion category arising from the subfactor.