2016/04/30 by Skip Garibaldi, Robert M. Guralnick, Daniel K. Nakano · 6 citations
Mathematics · #(g,K)-module #Advanced Algebra and Geometry #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Converse #Degeneracy (biology) #Field (mathematics) #Finite Group Theory Research #Fundamental representation #Geometry #Irreducible element #Irreducible representation #Lie algebra #Mathematical analysis #Mathematics #Pure mathematics #Representation (politics) #Representation theory #Representation theory of SU #Verma module #Weight #math.RT #msc:20C20 #msc:20G05
paper · pdf · doi:10.1016/j.jalgebra.2016.11.038
published in Journal of Algebra 477, 69-87 (Elsevier BV)
openalex publication_date 2017/01/04 · arxiv created 2018/09/25 · arxiv updated 2018/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 E8 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.