[GAP Forum] decomposing regular representation + (AREP package)

[Markus Pueschel]

Hi R.N.,

I am one of the authors of AREP:
http://www.ece.cmu.edu/~smart/arep/arep.html
AREP indeed only runs with gap3 but it can do what you want as long as the
group is solvable. It can give you F and also a fast algorithm for F, i.e.,
a factorization of F into a product of structured sparse matrices.
Unfortunately, we have no resources to port AREP to gap4 but you could
install gap3.

Markus

> -----Original Message-----
> From: forum-bounces at gap-system.org [mailto:forum-bounces at gap-system.org]
> On Behalf Of R.N. Tsai
> Sent: Saturday, February 24, 2007 4:55 AM
> To: GAP
> Subject: [GAP Forum] decomposing regular representation + (AREP package)
> 
> Dear gap forum,
> 
>   I would like to decompose the regular (permutation) representation of
> some small groups into irreducible representations (over the complexes).
> 
>   That is for finite group G of order |G|, I would like an explicit
> |G|x|G| matrix F such that
> 
>     F^-1 R(g) F = B(g)
> 
>   R(g) is the regular representation, B(g) is block diagonal.
>   R(g),B(g) and F are all |G|x|G| matrices over complexs.
> 
>   Is there anything in GAP that would facilitate getting such a matrix
> explicitly?
> 
> I ran accross a GAP3 package "AREP" but I'm not sure if that has what I
> need (I didn't read through all its documentation yet); it also doesn't
> look
> like it's supported by GAP4 anyway, so it may not be easily usable even if
> it did.
> 
>   Thanks for your help.
> 
>   R.N.
> 
> 
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