[GAP Forum] Finding the Sp(4,2)-orbits

[Kashyap Rajeevsarathy]

Thanks for your response. I apologize for not accurately framing my
question. Here is the context in which I asked this question :

Let $x_i, y_i$ be the generators of $H = Z^4$.* I need to compute the
Sp(4,2)-orbits of $(x_1 \wedge y_1) ^{ \otimes 2}$ and ${(x_1 \wedge y_1)
 + (x_2 \wedge y_2)}^{\otimes2}$ with respect to the diagonal
Sp(4,2)-action on $\wedge^2 H \otimes \wedge ^2H$ (modulo 2)* (\otimes2
refers to the tensor squared and Z refers to ring of integers) .

I would greatly appreciate if you could guide me about the best possible
way to do this in GAP starting with how to do the following:

1. tensor products of modules
2. wedge products of modules
3. diagonal actions as the ones mentioned above
4. If this requires additional programming, what might be the best way to
go about it?
5. Also, could I make GAP display the elements in the orbits in some
convenient fashion (like x_1^2 + y_1^2 etc. ).
6. In general, is it possible to make GAP display vectors in the orbits of
matrix actions simply as vectors (say [1,1,1,0]  etc. ).

Thanks,
Kahsyap

On Mon, Aug 20, 2012 at 5:20 PM, Dima Pasechnik <dima at ntu.edu.sg> wrote:

> On Mon, Aug 20, 2012 at 07:06:15PM +0800, Kashyap Rajeevsarathy wrote:
> > Hello,
> >
> > I am new to GAP and I was wondering if GAP could help me figure out the
> > following:
> >
> >  I would like to know the GAP command for enlisting the orbits of the
> > Sp(4,2)-action on (Z/2Z)^4, where Z/2Z is the field of order 2.
>
> gap> G:=Sp(4,2);
> gap> Orbits(G,FullRowSpace(GF(2),4));
>
> will do what you'd like to.
>
> However, Sp(2n,2) has just one orbit on nonzero vectors in its
> natural action, no need to ask GAP, in fact...
>
> HTH,
> Dmitrii
>
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-- 
Kashyap Rajeevsarathy
Assistant Professor,
IISER Bhopal, ITI (Gas Rahat) Building,
Govindpura, Bhopal - 462023,
Madhya Pradesh, India.