Irreducibility of automorphic Galois representations of GL(n), n at most 5

By Frank Calegari, T. Gee. 2011

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Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL_n(A_F), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to pi are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to pi are also irreducible. We also show that the Lie algebras of the Zariski closures of the l-adic representations are independent of l.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/268212b8693e22d4f0e8f8e5fb17a3ad08c5f975