Rational rigidity for E_8(p)

Abstract

We prove the existence of certain rationally rigid triples E8 in good characteristic and thereby show that these groups over the prime field occur as Galois groups over the field of rational numbers. We show that these triples give rise to rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic 0. As a byproduct we derive a remarkable symmetry between the character table of a finite reductive group and that of its dual group. We also give a classification of possible overgroups in exceptional groups containing regular unipotent elements.

The triples considered for F4 in the first paper are shown not to generate F4(p) but rather generate a subgroup contained in a parabolic subgroup over the prime field

References in corpus (1)

• Rigid local systems and relative motives with Galois group G_2

Cited by in corpus (4)

• Unipotent elements forcing irreducibility in linear algebraic groups
• Overgroups of regular unipotent elements in reductive groups
• Hesselink normal forms of unipotent elements in some representations of classical groups in characteristic two
• Rigidity for F_4(p)