  Let $k$ be a totally real field, and let $A/k$ be an absolutely irreducible,
polarized Abelian variety of odd, prime dimension whose endomorphisms are all
defined over $k$. Then the only strictly compatible families of abstract,
absolutely irreducible representations of $\gal(\ov{k}/k)$ coming from $A$ are
tensor products of Tate twists of symmetric powers of two-dimensional
$\lambda$-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.
