Talk:Character theory/Archive 1

No context
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 — Preceding unsigned comment added by 193.55.38.129 (talk) 10:36, 02 December 2004 (UTC)


 * 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, 02 December 2004 (UTC)

Expanding the article
Some suggestions for where to go next - the completeness of the article could be improved by including material on: --Michael Stone 00:23, 20 May 2005 (UTC)
 * 1) Definition of the kernel of a character.
 * 2) Lifted characters.
 * 3) Restriction of a character to a subgroup.
 * 4) The permutation character.
 * 5) Linear vs. non-linear characters.
 * 6) Irreducibility of characters.
 * 7) Linear characters are the lifts of irreducible characters of normal subgroups.
 * 8) 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).
 * 9) The connections between characters and algebraic integers, in particular, the roots of unity.


 * 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)

Notation problem in orthogonality relation
In the paragraph that reads

The orthogonality relation for columns is as follows:
 * For $$g, h \in G$$ the sum $$\sum_{\chi_i} \chi_i(g) \overline{\chi_i(h)} = \begin{cases}\left | C_G(g) \right |, & \mbox{ if } g, h \mbox{ are conjugate } \\ 0 & \mbox{ otherwise.}\end{cases}$$

where the sum is over all of the irreducible characters $$\chi_i$$ 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.


 * Right, the symbol C_G(g) was not defined - it means the size of the conjugacy class. And there is a factor 1/|G| missing. And the orthogonality of rows was not actually stated. I've fixed these now. Paul Matthews 09:27, 21 November 2006 (UTC)

More expansion
(It would be good to have:)
 * 1) A more extensive list of the character tables of important groups, such as the symmetric and alternating groups. —Preceding unsigned comment added by 131.111.233.70 (talk) 20:36, 25 February 2008 (UTC)