Dear R.N.Tsai, dear forum, the main problem here is to obtain the complete list of irreducible complex representations of G. IMHO computing the latter is a rather nontrivial question for arbitrary finite groups. Once you know such a list, computing F is straightforward. See e.g. Sect. 2.7 of J.-P. Serre, Linear representations of finite groups. Graduate Texts in Mathematics, Vol. 42, Springer, New York, 1977
I have some GAP4 code (that I can make available upon request, although it's not in any kind of polished form) that implements these formulae; we used it in just completed preprint http://www.ntu.edu.sg/home/dima/papers/truss6.pdf where you can also find these formulae from Serre's book. Actually, there it is used to compute a decomposition into irreducibles, and then the centraliser ring, of a finite group representation, so it's a slightly more general problem than yours. Best, Dmitrii http://www.ntu.edu.sg/home/dima/ On 2/24/07 5:54 PM, "R.N. Tsai" <[EMAIL PROTECTED]> wrote: > 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. _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
