Quark and lepton assignments in theE7model

Abstract

The embedding of the SU(2) × U(1) × ${\mathrm{SU}\left(3\right)\mathrm{}}^{\mathrm{color}}$ group of weak and electromagnetic innteractions and chromodynamics into the gauge group ${\mathrm{E}}_7$ is discussed in terms of the various possibilities for quark and lepton assignments, including heavy quarks and heavy leptons. It is shown that there is at least one assignment, defined up to a few mixing angles, which agrees with the existing weak-interaction phenomenology. The octonionic structure of the assignment is also exhibited and related to the exceptional observables of Jordan, von Neumann, and Wigner.