[GAP Forum] Failed to run AreRepsIsomorphic command.

[Hongyi Zhao]

On Sat, Apr 30, 2022 at 5:34 PM Dima Pasechnik <dima at sagemath.org> wrote:
>
> On Sat, Apr 30, 2022 at 05:21:22PM +0800, Hongyi Zhao wrote:
> > >
> > > AreRepsIsomorphic does not take lists of representations as arguments, it takes individual
> > > representations.
> > >
> > > It is meant to be used on representations with the same underlying group, in your setting it might not work
> > > (say, because different generators are used).
> >
> > I still don't know how to use it. Please see my example below:
> >
> > gap> LoadPackage("RepnDecomp");
> > true
> > gap> g:=CyclicGroup(IsFpGroup,8);
> > <fp group of size 8 on the generators [ a ]>
> > gap> AreRepsIsomorphic(IrreducibleRepresentations(g));
> > Error, Function: number of arguments must be 2 (not 1)
> > not in any function at *stdin*:12
> > type 'quit;' to quit to outer loop
>
> wrong arguments passed, as you should be able to read from the error
> message. Here is something that works:
>
> gap> ir:=IrreducibleRepresentations(g);
> gap> AreRepsIsomorphic(ir[1],ir[2]);

It does the trick, as shown below:

gap> g:=CyclicGroup(IsFpGroup,8);
<fp group of size 8 on the generators [ a ]>
gap> ir:=IrreducibleRepresentations(g);
[ Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ 1 ] ], [ [ 1 ] ], [ [ 1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ -1 ] ], [ [ 1 ] ], [ [ 1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ E(4) ] ], [ [ -1 ] ], [ [ 1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ -E(4) ] ], [ [ -1 ] ], [ [ 1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ E(8)^3 ] ], [ [ E(4) ] ], [ [ -1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ -E(8)^3 ] ], [ [ E(4) ] ], [ [ -1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ -E(8) ] ], [ [ -E(4) ] ], [ [ -1 ] ] ],
  Pcgs([ a^7, a^2, a^4 ]) -> [ [ [ E(8) ] ], [ [ -E(4) ] ], [ [ -1 ] ] ] ]
gap> AreRepsIsomorphic(ir[1],ir[2]);
false

Another question: How to obtain a pretty formatted output of
IrreducibleRepresentations?

> HTH,
> Dima

Yours,
Hongyi