1
$\begingroup$

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?

$\endgroup$
0

1 Answer 1

3
$\begingroup$

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) >;

$\endgroup$
2
  • $\begingroup$ 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, 2012 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, 2012 at 20:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.