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

[Dmitrii (Dima) Pasechnik]

It is a (documentation, at least) bug in both GAP 4.4 and in
GAP 4.5; in the latter
(more precisely, GAP 4.5.4)
I get

gap> IrreducibleRepresentations(DihedralGroup(10),GF(2^2));
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `[]' on 2 arguments called from
s = 1 called from
LiftAbsAndIrredModules( pcgsS, pcgsN, modrec, dim ) called from
AbsAndIrredModules( G, F, dim ) called from
IrreducibleModules( G, f, 0 ) called from
<function "unknown">( <arguments> )
 called from read-eval loop at line 5 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>

Hopefully someone who knows more about the algorithms involved can
comment on this, and/or provide a fix.

Best,
Dmitrii

On 13 July 2012 01:38, Neha Makhijani <nehamakhijani at gmail.com> wrote:
> 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
>