I am trying to look at a representation (so a homomorphism) of a group G, and see what the restriction of the representation to a subgroup of G will be. Is there an easy way (or any way!) to do this in MAGMA?
If your representation R is of type Map (which it will be if you defined it as Representation(M) for a G-module M), then to restrict R to subgroup H
RH := map< H->Codomain(R) | x :-> R(x) >;
If you have defined R as a group homomorphism G -> GL(n,K) for some field K, then you could instead use
RH := hom< H->Codomain(R) | x :-> R(x) >;