# Homomorphisms and their restrictions in MAGMA

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?

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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) >;

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) >;

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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> – dward1996 Jan 5 '12 at 16:47
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 >; – Derek Holt Jan 5 '12 at 20:09
Thanks for clarifying things. – dward1996 Jan 7 '12 at 9:27