Welcome to MathOverflow

Question

1

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?

edited Mar 27 2012 at 18:42

Max
2,227●8●15

asked Jan 5 2012 at 14:45

dward1996
189●8

Derek Holt · Accepted Answer · 2012-01-05 16:31:41Z UTC

2

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) >;

edited Jan 5 2012 at 16:31

answered Jan 5 2012 at 16:25

Derek Holt
6,858●1●12●27

	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 2012 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 2012 at 20:09
	Thanks for clarifying things. – dward1996 Jan 7 2012 at 9:27

Homomorphisms and their restrictions in MAGMA

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.