Work

Rational rigidity for

Year: 2014

Type: article

Abstract: 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.

Source: Compositio Mathematica

DOI: 10.1112/s0010437x14007271

Authors: Robert Guralnick, Gunter Malle

Institutions: University of Southern California, University of Kaiserslautern

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Simons Foundation, FP7 Ideas: European Research Council

Awards: G1227956904, Counting conjectures and characters of almost simple groups, Presentations, Cohomology and Representations of Finite Groups and Coverings of Curves, G8213256141