1 results
Rational rigidity for
${E}_{8}(p)$
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 10 / October 2014
- Published online by Cambridge University Press:
- 17 July 2014, pp. 1679-1702
- Print publication:
- October 2014
-
- Article
- Export citation
-
We prove the existence of certain rationally rigid triples in
${E}_{8}(p)$ for good primes 
$p$ (i.e. 
$p>5$) thereby showing that these groups occur as Galois groups over the field of rational numbers. We show that these triples arise from rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic zero. As a byproduct of the proof, we derive a remarkable symmetry between the character table of a finite reductive group and that of its dual group. We also give a short list of possible overgroups of regular unipotent elements in simple exceptional groups.
