Talk:Induced representation

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This page is a bit technical and needs some cleaning up. It would help if there was an introductory paragraph on how induced representations of finite goups works with examples.

Yes, the page's evolution hasn't been particularly kind to it. Various things: the Frobenius character formula isn't given. More obscurely, there is a way of computing with induced representations allied to coset enumeration (it's coset enuneration with some labelled edges) which is John Conway's point of view and a good counterbalance to abstract discussion. Charles Matthews 14:09, 10 November 2005 (UTC)

See system of imprimitivity, where these are discussed for finite groups first.--CSTAR 15:24, 10 November 2005 (UTC)

[edit] The current state of the article

I had to use this article when writing about principal series representations of semisimple Lie groups for the article Zonal spherical function. The definition of induced representation was wrong for induction from a non-compact subgroup, even when all groups are discrete and countable (eg for Shimura's definition of Hecke operators). It was wrong even in the case of one dimensional characters induced from the integers to the real numbers. Although I don't have time at the moment, it would be nice to have some references, such as the various books and articles by George Mackey, including the books based on his Chicago and Oxford lecure notes, as well as giving the origins of the theory for topological groups, which I have always understood to have been the Stone-von Neumann theorem (see also Varadajan's book, "he Geometry of Quantum Theory"). I don't have time to provide references for this article or to improve it any more at present, but it would be nice if somebody could fully correct the topological part using the references I have cited, or other references by Blattner, Fell or Rieffel. Mathsci (talk) 04:35, 4 June 2008 (UTC)