Talk:Character theory
From Wikipedia, the free encyclopedia
In the first line, articles says "of the representation given above". Alas, no representation is given. Is it on purpose ? I'll try to write one when I have time. user michaelmestre
- Yes, the text of this page was cut and pasted rather poorly from group representation. The context for the statement can be found there. -- Fropuff 16:37, 2004 Dec 2 (UTC)
[edit] Expanding the article
Some suggestions for where to go next - the completeness of the article could be improved by including material on:
- Definition of the kernel of a character.
- Lifted characters.
- Restriction of a character to a subgroup.
- The permutation character.
- Linear vs. non-linear characters.
- Irreducibility of characters.
- Linear characters are the lifts of irreducible characters of normal subgroups.
- Irreducible characters as a basis for the vector space of class functions (i.e. complex-valued functions which are constant on conjugacy classes of the group).
- The connections between characters and algebraic integers, in particular, the roots of unity.
--Michael Stone 00:23, 20 May 2005 (UTC)
- Sounds good to me. Even a few sentences on each would be great; and even full articles if/when a lot can be said. linas 04:51, 20 May 2005 (UTC)
In the paragraph that reads
The orthogonality relation for columns is as follows:
- For
the sum 
where the sum is over all of the irreducible characters χi of G
the symbol group C_G(g) looks suspicious. I dare not edit, however, not sure of what was intended. 212.194.88.242 20:21, 16 January 2006 (UTC) Bossavit, CNRS.
