Talk:Modular representation theory

What about representations from modular forms, or rather their Jacobians + the Shimura construction of a related elliptic curve. I am just asking about disambiguation ...

Field notation

Notation - Z₂ isn't the best choice here for the field with two elements, since Brauer lifting (if I have the right term) is a basic thing in the theory and would concern lifting of modular representations, in this case, to representations over the 2-adic integers. So at some later point this would all get confusing. F_p for a [[Galois field] should be better.

Charles Matthews 12:06, 2 Apr 2005 (UTC)

Brauer lifting

I think we should actually add a section on "Brauer lifting" (I've no idea either whether this is the right term, but I think the meaning is quite obvious), Brauer characters etc. My main problem, though, is to fit this into the existing structure of the article, as - for example - the lifting technique is useful for _any_ representation in positive characteristic (and not only if the characteristic divides the group order).

Helena (alias HW)

There's a basic technical result on lifting idempotents, isn't there? Charles Matthews 18:49, 29 Apr 2005 (UTC)

General versus important specific cases

This page is currently written in very general terms mainly from the perspective of block theory developed in the spirit of Brauer- what might be called the modular representation theory of the general finite group. It could be much expanded by discussing the various links with representation theory of particular types of groups: eg symmetric groups, finite groups of Lie type. Also the necessity to study representation theory of related algebraic objects- eg quantum groups, complex reflection groups, to understand representations of particular groups. This could get too technical very easily of course, but nevertheless it would be nice if someone (or some people) could indicate the spirit of some of the modern developments here or provide links if such things are developed elsewhere. Messagetolove 13:52, 7 May 2007 (UTC)

-The main reason why I haven't done this is because I have a job. If I had a spare year I would get round to sorting out all this stuff, but I'd rather spend it writing articles. Seriously though, you're talking a major undertaking here. I think this is suitably general for an encyclopaedia. We wouldn't want to start discussing the representation theory of the groups of Lie type for example, because it's too specialized and everyone who wants to know about that already has access to libraries I would think. Davcrav 10:19, 14 May 2007 (UTC)

I guess I was viewing WP as a long-term collaborative effort, not commenting on the work-to-date of any individual, nor suggesting that any individual do anything in particular. I spent quite a bit of time on this article myself, but so far from the "general" perspective. In some cases, what I indicated on the wish-list above may just be a question of putting links in, or could become a question of that if other appropriate articles were written. I was thinking that the non-specialist ought to be told, possibly in very general terms, that there are other facets to the subject.

Messagetolove 12:38, 14 May 2007 (UTC)

Applications to coding theory

'modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory'. I am working in the field of coding theory and I do not know of any applications of modular representation theory in coding theory. Can you, please, supply references? — Preceding unsigned comment added by 132.67.250.210 (talk) 13:07, 25 October 2011 (UTC)

MR1749525 uses modular reps to decide if a code is MDS. MR1285209 is a book on the application of modular representation theory to coding theory. JackSchmidt (talk) 20:28, 1 November 2011 (UTC)