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Orbifold subfactors from Hecke algebras. (English) Zbl 0805.46077

Summary: We apply the notion of orbifold models of \(SU(N)\) solvable lattice models to the Hecke algebra subfactors of Wenzl and get a new series of subfactors. In order to distinguish our subfactors from those of Wenzl, we compute the principal graphs for both series of subfactors. An obstruction for flatness of connections arises of this orbifold procedure in the case \(N= 2\) and this eliminates the possibility of the Dynkin diagrams \(D_{2n+1}\), but we show that no such obstructions arise in the case \(N=3\). Our tools are the paragroups of Ocneanu and solutions of Jimbo-Miwa-Okado to the Yang-Baxter equation.

MSC:

46N50 Applications of functional analysis in quantum physics
81T25 Quantum field theory on lattices
46L60 Applications of selfadjoint operator algebras to physics
81T10 Model quantum field theories
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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