Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type ${\mathsf{E}}_6$ and ${\mathsf{E}}_7$ simple Lie algebras

Robert G. Donnelly, Molly W. Dunkum, Austin White

We construct every finite-dimensional irreducible representation of the simple Lie algebra of type ${\mathsf{E}}_7$ whose highest weight is a nonnegative integer multiple of the do…