> < ^ Date: Thu, 10 Feb 2000 13:43:52 -0500
> < ^ From: Markus Pueschel <pueschel@earthlink.net >
> < ^ Subject: Re: matrices with integer entries modulo n

Dear Gap Forum,

Jurgen Muller wrote:
> Dear Gap Forum, dear Edgar,
> > I am interested in finding the irreducible representations of GL(2,n) -
> > the group of 2-by-2 invertible matrices with integer entries modulo n.
> > Here, n is not necessarily a power of a prime number. How can I use Gap
> > to find these irreducible representations?
> As far as I know, up to now there is no built-in automatic mechanism
> in GAP to compute the irreducible representations of an arbitrary
> finite group. (The situation is different for special classes of
> groups, which unfortunately the GL_2(Z/nZ)'s do not belong to.) But
> there are so-called `MeatAxe' techniques available to find irreducible
> representations rather comfortably by hand. There is a GAP share
> package which works over finite fields, and I have (private, still)
> programs which (are supposed to) do the job over the rationals and
> finite extension fields thereof.
> These programs might be useful for the examples you have, Edgar; if
> you are interested, please do not hesitate to contact me. Possibly I
> can then give you more specific advice.
> Best, J"urgen M"uller.
If the group is solvable, then a full set of irreducible
representations can be computed using the package AREP:
List(Irr(g), chi -> ARepWithCharacter(chi));
Unfortunately, AREP is currently only for GAP 3.4.4 available.

Best, Markus
Markus Pueschel
Carnegie Mellon University
5000 Forbes Ave 
Pittsburgh, PA 15213
phone: (412) 268 3804
fax (412) 268 3890

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