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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)
Too technical notice: actually group representation is the general introduction. Charles Matthews 21:17, 28 October 2005 (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)
This section requires cleanup:
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)
This article is rated B-class on Wikipedia's
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This article links to one or more target anchors that no longer exist.
Please help fix the broken anchors. You can remove this template after fixing the problems. |
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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)
Too technical notice: actually group representation is the general introduction. Charles Matthews 21:17, 28 October 2005 (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)
This section requires cleanup:
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)