On Sat, Apr 30, 2022 at 4:44 PM Bill Allombert
<bill.allomb...@math.u-bordeaux.fr> wrote:
>
> On Sat, Apr 30, 2022 at 03:21:10PM +0800, Hongyi Zhao wrote:
> > Hi GAP team,
> >
> > I use the following code snippet to compute the irreducible characters
> > of a finitely presented group:
> >
> > So, I want to get a pretty printed result with the rows correspond to
> > irreducible representations, and the columns correspond to conjugacy
> > classes of group elements.
> >
> > Are there any clues to achieve this goal?
>
> Use Display(CharacterTable(g));
>
> gap> G:=CyclicGroup(8);
> <pc group of size 8 with 3 generators>
> gap> Display(CharacterTable(G));
> CT1
>
> 2 3 3 3 3 3 3 3 3
>
> 1a 8a 4a 2a 8b 8c 4b 8d
>
> X.1 1 1 1 1 1 1 1 1
> X.2 1 -1 1 1 -1 -1 1 -1
> X.3 1 A -1 1 -A A -1 -A
> X.4 1 -A -1 1 A -A -1 A
> X.5 1 B A -1 -/B -B -A /B
> X.6 1 -B A -1 /B B -A -/B
> X.7 1 -/B -A -1 B /B A -B
> X.8 1 /B -A -1 -B -/B A B
>
> A = E(4)
> = Sqrt(-1) = i
> B = E(8)
See the following results in my example
gap> f := FreeGroup( "p", "q");;
gap> g42:= f/[ [ f.1 , f.1^-1 ], [ f.2 , f.2^-1 ], [ f.2 *f.1, f.1 *f.2 ] ];
<fp group on the generators [ p, q ]>
gap> Display(CharacterTable(g42));
CT1
2 2 2 2 2
1a 2a 2b 2c
2P 1a 1a 1a 1a
X.1 1 1 1 1
X.2 1 -1 -1 1
X.3 1 -1 1 -1
X.4 1 1 -1 -1
Now, I'm confused on the following lines shown above:
2 2 2 2 2
1a 2a 2b 2c
2P 1a 1a 1a 1a
1. What's the meaning of all 2's in this line?
2 2 2 2 2
2. What's the meaning of 1a, 2a, 2b, 2c, and 2P, respectively?
> Cheers,
> Bill.
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