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 Gmodule M), then to restrict R to subgroup H
RH := map< H>Codomain(R)  x :> R(x) >;
should work.
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) >;

$\begingroup$ Thanks for the helpful response. Sorry for my ignorance (but I am very new to MAGMA), but if I have the homomorphism G>GL(n,K) as above, and G is defined in terms of generators a and b (with images say x and y), would I define the homomorphism as follows: hom<G>GL(n,k)a:>x,b:>y> $\endgroup$ – dward1996 Jan 5 '12 at 16:47

$\begingroup$ No, the correct syntax for that is hom<G>GL(n,k) <a,x>, <b,y> > or if a,b are the Magma's stored generators G.1, G.2, then you can just write hom<G>GL(n,k) x, y >; $\endgroup$ – Derek Holt Jan 5 '12 at 20:09