Talk:Real representation
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Initial comments
editBy the way, should that be k = 0, 1, 2, ... ?
Charles Matthews 15:28, 24 Jun 2004 (UTC)
While it is true a real reps can be constructed from complex reps, shouldn't an article on real reps treat them intrinsically as reps over R without mentioning C? Phys 21:46, 6 Aug 2004 (UTC)
I agree about real reps being defined over R rather than C. I will edit the page accordingly if no-one objects. What it says at the moment is ambiguous (one that also allows ... sounds like two conditions). JAMnx 13:29, 18 March 2007 (UTC)
nth Frobenius-Schur indicator
editThere's a typo in the formula for the n-th indicator. It should have \rho(g^n), not \rho(g)^n, right? (Tr(A^n) != (Tr(A))^n) And what is a self-intertwiner?
Sorry. Of course \rho(g^n) = \rho(g)^n, since \rho is a group homomorphism. Numenorean7 13:18, 25 April 2007 (UTC)
Also, the Frobenius-Schur indicator is originally given using the Harr measure, but then these later formulas are specialized to finite groups.
Perhaps after the indicator is first introduced the sum for the special case of a finite group should be given.
Also, I would REALLY like a reference to a book. Is there a "standard" reference for real representation theory?
BTW, I'm a wiki-newby so I don't really know how this works. 134.114.148.104 23:58, 23 April 2007 (UTC)
- Feit, Characters of Finite Groups, p.21, Dornhoff, Group Representation Theory A, p.191, have the basic result. Charles Matthews 15:16, 25 April 2007 (UTC)
Maths and physics
editThe idea that real representations are real vector spaces in mathematics and complex vector spaces in physics is at best an oversimplification and I doubt it stands up to any scrutiny in reliable sources. For instance, Majorana and Majorana-Weyl spinors are real representations in physics, and are certainly real vector spaces. I'm rewriting the article accordingly. Geometry guy 11:08, 21 September 2008 (UTC)
Reference to Serre misleading?
editIMHO, the reference to the book of Serre is misleading. This book rather deals with rational representations (and thereby with real ones) but not in a context together with representations of real/complex/quaternionic type and with complex (conjugate) vector spaces as one would expect in retrieving this article.
It is really sad that there is so little to be found in literature about (ir)reps of those three types. The still best one I checked out is the book of Bröcker/tom Dieck on reps of compact groups (a large chapter), and also a small section in Cornwell I.