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'abstract' Homomorphisms of L-adic Groups and Abelian Varieties

Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphism rings is non-trivial and is defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic representations plus field automorphisms. The main ingredients of the proofs are the work of Borel and Tits on the 'abstract' homomorphisms of almost simple algebraic groups, plus the work of Shimura on the fields of moduli of Abelian varieties.