Talk:Character theory/Archive 1

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:

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.

--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)

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)