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) >;
answered Jan 5, 2012 at 16:25
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$\begingroup$ 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> $\endgroup$ Commented Jan 5, 2012 at 16:47
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$\begingroup$ 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 >; $\endgroup$ Commented Jan 5, 2012 at 20:09