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Orbifold subfactors from Hecke algebras

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Abstract

We apply the notion of orbifold models ofSU(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 in this orbifold procedure in the caseN=2 and this eliminates the possibility of the Dynkin diagramsD 2n+1 , but we show that no such obstructions arise in the caseN=3. Our tools are the paragroups of Ocneanu and solutions of Jimbo-Miwa-Okado to the Yang-Baxter equation.

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Author notes

  1. Yasuyuki Kawahigashi (Miller Research Fellow)

    Present address: Department of Mathematical Sciences, University of Tokyo, Hongo, 113, Tokyo, Japan

Authors and Affiliations

  1. Department of Mathematics, University College of Swansea, Singleton Park, SA2 8PP, Swansea, Wales, U.K.

    David E. Evans

  2. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Yasuyuki Kawahigashi (Miller Research Fellow)

Authors
  1. David E. Evans
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  2. Yasuyuki Kawahigashi
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Communicated by N. Yu. Reshetikhin

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Evans, D.E., Kawahigashi, Y. Orbifold subfactors from Hecke algebras. Commun.Math. Phys. 165, 445–484 (1994). https://doi.org/10.1007/BF02099420

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