[GAP Forum] Decomposing direct products of reps into irreps

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Krishna,

Presuming you are talking about representations over complex numbers,
GAP can easily tell you with which multiplicities the irreducible
representations appear
in the representation P you have. For this you just need to compute
its character x(P).
Then computing the scalar products of x(P) with the characters of the
irreducible
representations (available in the character table) of your group will
give you this information.

Doing the actual decomposition into the direct sum of the irreducibles
is also doable
by the brute-force method described e.g. in the 1st part of J.Serre's
book "Linear representations of finite groups" (look for "explicit
decomposition of a representation"),
but there seems to be no GAP code publicly available that actually
does this computation.
(I wrote such code a while ago, and could e-mail it to you, although
it's by no means
finished or anything...)

Best,
Dmitrii



On 19 March 2010 01:07, krishna mohan <trebauchet1986 at yahoo.co.in> wrote:
> Hi.....
>
>
>         Suppose I take the direct product of two two-dimensional representations of D4...and then I want to decompose it as direct sum of irreducible representations of D4........
>
> I need to do such decompositions quite often for my current project...
>
> So I was wondering if GAP has anything built in to tackle the above task...
>
> I searched the manual but came up with nought....
>
> Krishna
>
>
>
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--
Dmitrii Pasechnik
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