[GAP Forum] computations of characters

[Stefan Witzel]

Hello,

I'm new to this list and in fact I'm also new to GAP. But I've been told that if there is anyone knowing how I could accelerate my computation, he will probably read this list.
What I try to do is
1) compute irreducible characters of SU(n,q) and
2) compute induced characters of trivial characters of stabilizers in SU(n,q).

I started of by just taking

  G := SU(n,q); and computing
  Irr(G);

(Id did not quite use the built-in version but that probably doesn't matter here). A colleague found out, that it is faster to get a permutation description by letting

  V := GF(q^2)^n;
  v := Basis(V)[1];
  orb:=SortedList(Orbit(Gsu,v,OnPoints));
  hom := ActionHomomorphism(G,orb,OnPoints); 
  Gperm := Image(hom);

and then taking Gperm instead of G.
For the induced characters it is pretty much the same: If H is the stabilizer (a group of block-diagonal matrices), I used to compute

  InducedClassFunction(TrivialCharacter(H),G)

and know I compute

  Hperm := Image(hom,H);
  InducedClassFunction(TrivialCharacter(Hperm),Gperm);

and it is also faster.

Of course it is still too slow (as it is always) and my question is, if anybody has an idea how to accelerate one of these computations? Thanks in advance for suggestions!

Regards,
Stefan Witzel