> < ^ From:

> < ^ Subject:

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 http://avalon.ira.uka.de/home/pueschel/

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