> < ^ Date: Thu, 01 Apr 1993 12:55:40 +0200
> < ^ From: Joachim Neubueser <joachim.neubueser@math.rwth-aachen.de >
^ Subject: Representation Theory in GAP

In his letter Peter Webb writes:

On the topic of representation theory within GAP, I have the impression
that this side of things has been somewhat neglected so far. The meataxe
is implemented, but I have other goals in mind to do with creating software
to complement this. For example, the meataxe would not be so good for
analyzing the structure of modules for p-groups in characteristic p, but
algorithms based upon the computation of fixed points are very effective in
this situation. It is a long-term project for me to expand what software
I have, and to put it into a publicly acceptable state. Right now, for
example, it does not properly conform to the object-oriented style of GAP,
and it is not adequately tested. At this point I would be happy to hear of
others writing similar software (some I already know of). My general aim
is to have a package which computes Loewy series reasonably, will extract
a quotient in the Loewy series of a p-group as a representation of its
normalizer in a larger group (for example), will compute relative traces
between modules of fixed points, and such similar things.

We agree. While character theory (and hence ordinary representation
theory) is rather well represented in GAP, working with modular
representations is not yet. Note however that there is a link to the
MOC system for working with modular characters provided in GAP (see
section 42.46 ff, p.679 of the manual). We do intend to extend
facilities for working in modular representation theory and we will
welcome cooperation with others who have already implemented routines
or are implementing routines in this field. We will contact Peter
Webb directly but also ask others who are interested to contact us,
e.g. Klaus Lux or Herbert Pahlings (lux@math.rwth-aachen.de ,
pahlings@math.rwth-aachen.de) and we hope that eventually we will be
able to provide a good package.

Joachim Neubueser

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