Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups · arXivDesk
1712.05528Dec 15, 2017This paper replaces "Lübeck's classification of Chevalley groups representations and the inverse Galois problem for some orthogonal groups" arXiv:1712.05528v2. Revised version - referees' comments added. The final version is to appear in J. Number Theory
Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups
In this paper we prove that for each integer of the form n=4ϖ (where ϖ is a prime between 17 and 73) at least one of the following groups: PΩn+(Fℓs)
Nearby in the stack
,
PSOn+(Fℓs)
,
POn+(Fℓs)
or
PGOn+(Fℓs)
is a Galois group of
Q
for almost all primes
ℓ
and infinitely many integers
s>0
. This is achieved by making use of the classification of small degree representations of finite simple groups of Lie type in defining characteristic of F. Lübeck and a previous result of the author on the image of the Galois representations attached to RAESDC automorphic representations of