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

2011/04/25 by Frank Calegari, Calegari, Frank, Toby Gee +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1104.4827

Abstract

Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic\nrepresentation of GL_n(A_F), where F is a totally real field and n is at most\n5. We show that for all primes l, the l-adic Galois representations associated\nto pi are irreducible, and for all but finitely many primes l, the mod l Galois\nrepresentations associated to pi are also irreducible. We also show that the\nLie algebras of the Zariski closures of the l-adic representations are\nindependent of l.\n

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