English

Globally Irreducible Weyl Modules

Representation Theory 2018-09-27 v3

Abstract

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 E8E_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.

Keywords

Cite

@article{arxiv.1604.08911,
  title  = {Globally Irreducible Weyl Modules},
  author = {Skip Garibaldi and Robert M. Guralnick and Daniel K. Nakano},
  journal= {arXiv preprint arXiv:1604.08911},
  year   = {2018}
}
R2 v1 2026-06-22T13:44:50.905Z