Talk:Representation theory of finite groups
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This page could do with an introduction. -- Fropuff 16:07, 2004 Aug 9 (UTC)
Well, it could do with taking in hand.
(Actually ANY finite dimensional rep of a finite group can be turned into a unitary rep. To see this, note that any finite dimensional space can be turned into a Hilbert space with a positive definite sesquilinear form <.,.>. The same thing too with the rep, but then it needn't necessarily be unitary. But we can construct a new positive definite sesquilinear form which makes it unitary).
I've just written this in different words at unitary representation. It's an argument only available over the complex numbers, so probably belongs there.
Charles Matthews 18:43, 20 Sep 2004 (UTC)
- Also, I have added a simple example, near the top in non-technical language. So I've taken out the technical notice. The page still needs some work lower down though. Paul Matthews 17:32, 22 November 2006 (UTC)
Under Constructing New Representations from Old, I think there is a mistake. Surely the direct sum is (p_1(g)v, p_2(g)w) rather than (p_1(g)v, p_1(g)w). Also, I do not see why the definition of subrepresentations is only over the complex numbers.
I came to this page to find out whether there exists a linear representation for every finite group. Shouldn't something like that be addressed here, or am I just too dense to find it? -GTBacchus(talk) 18:08, 13 December 2005 (UTC)
- The left regular representation is a faithful linear representation for any finite group. - Gauge 05:39, 9 January 2006 (UTC)
Application of Schur's lemma
This section requires cleanup:
- Needs an introduction
- Incredibly informal language
- Contradictory use of notation on at least two occasions
- The final theorem is false for every finite nontrivial group when the tensor product is taken to mean the standard tensor product of G-modules, so the original poster probably intends some other tensor product and that should be mentioned.
- Needs a source, since it is quite possibly original research, though it sounds vaguely familiar to an idea from modular representation theory
Most of the articles in this area need quite a bit of cleanup, so if this section cannot be sourced, it might be better to delete it. I just didn't want to delete it after cleaning it for 30 minutes. JackSchmidt (talk) 00:03, 5 December 2007 (UTC)