Additive Polynomials for Finite Groups of Lie Type
Group Theory
2015-10-29 v3 Representation Theory
Abstract
This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on results of Matzat which give bounds for Galois groups of Frobenius modules and uses the structure and representation theory of the corresponding connected linear algebraic groups.
Cite
@article{arxiv.0906.1380,
title = {Additive Polynomials for Finite Groups of Lie Type},
author = {Maximilian Albert and Annette Maier},
journal= {arXiv preprint arXiv:0906.1380},
year = {2015}
}
Comments
59 pages; v2: added reference, slightly restructured section 6.1, few small rewordings; v3: completed realization of Steinberg's triality groups (thanks to P. Mueller for solving the remaining open question); clarified argument how to use Thm. 3.4