[GAP Forum] irreducible representations of the dihedral group D10 over GF(4)

[Neha Makhijani]

It works for fields of non-prime order. But really not able to guess why it
does not work for this particular case. Have a look!

IrreducibleRepresentations(DihedralGroup(10),GF(2^3));
[ Pcgs([ f1, f2 ]) -> [ [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ] ],
  Pcgs([ f1, f2 ]) -> [
      [ [ Z(2)^0, 0*Z(2), Z(2^3), Z(2)^0 ], [ 0*Z(2), Z(2)^0, Z(2^3)^6,
               Z(2^3)^3 ], [ 0*Z(2), 0*Z(2), Z(2^3), Z(2^3)^3 ],
          [ 0*Z(2), 0*Z(2), Z(2^3)^2, Z(2)^0 ] ],
      [ [ Z(2^3)^2, Z(2^3)^4, Z(2^3), 0*Z(2) ],
          [ Z(2^3)^3, Z(2^3), 0*Z(2), Z(2^3) ],
          [ Z(2^3), Z(2^3), Z(2^3)^3, Z(2^3)^5 ],
          [ Z(2)^0, 0*Z(2), Z(2^3)^4, Z(2^3)^2 ] ] ] ]

Neha

On Thu, Jul 12, 2012 at 10:51 PM, Dmitrii (Dima) Pasechnik
<dima at ntu.edu.sg>wrote:

> This looks like a bug (in documentation, at least).
> This command apparently does not work for
> finite fields of non-prime order.
> (but you can still do IrreducibleRepresentations(DihedralGroup(10),GF(2)))
>
> Hope this helps,
> Dmitrii
>
> On 13 July 2012 00:58, Neha Makhijani <nehamakhijani at gmail.com> wrote:
> > Can somebody please clarify as to why I am not able to get the
> irreducible
> > representations of the dihedral group over GF(4)??
> >
> > IrreducibleRepresentations(DihedralGroup(10),GF(2^2));
> > List Element: <position> must be a positive integer (not a boolean)
> >
> > Thanks!
> >
> > Neha
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-- 
Neha Makhijani
Research Scholar
Department of Mathematics
IIT Delhi