Irreducibility of Weyl Modules over Fields of Arbitrary Characteristic

Skip Garibaldi, Robert M. Guralnick, Daniel K. Nakano

Published 2016-04-29Version 1

In the representation theory of split reductive algebraic groups, it is well known that every Weyl module with minuscule highest weight is irreducible over every field. Also, the adjoint representation of $E_8$ is also irreducible over every field. In this paper, we prove a converse to these statements, as conjectured by Gross: if a Weyl module is irreducible over every field, it must be either one of these, or trivially constructed from one of these.