JournalsprimsVol. 30 , No. 1DOI 10.2977/prims/1195166280

The <i>E</i><sub>7</sub> Commuting Squares Produce <i>D</i><sub>10</sub> as Principal Graph

  • David E. Evans

    University of Wales Cardiff, UK
  • Yasuyuki Kawahigashi

    University of Tokyo, Japan
The <i>E</i><sub>7</sub> Commuting Squares Produce <i>D</i><sub>10</sub> as Principal Graph cover

Abstract

We prove that the (two) connections, or commuting squares, on the Coxeter-Dynkin diagram _E_7 produce a subfactor with principal graph _D_10. This was conjectured by J.-B. Zuber in connection with modular invariants in conformal field theory, and solve the last case of computing the flat parts of the connections on Coxeter-Dynkin diagrams with index less than 4.