# 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

## 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.

## Cite this article

David E. Evans, Yasuyuki Kawahigashi, The <i>E</i><sub>7</sub> Commuting Squares Produce <i>D</i><sub>10</sub> as Principal Graph. Publ. Res. Inst. Math. Sci. 30 (1994), no. 1, pp. 151–166

DOI 10.2977/PRIMS/1195166280