On 2008-05-14, WC <cacher.in.the....@gmail.com> wrote:
> What is the relation between characters of a group and its subgroup?
> e.g. what is the relation between characters of E(8) [group] and E(7) > and SU(2) [Sub-groups]?
Well, a character is a function on a group, so given a character of the big group we get by restriction characters on any subgroup. Going the other way is called induction, see http://en.wikipedia.org/wiki/Character_theory or any book on representation theory, for instance Fulton and Harris. -- Maarten Bergvelt
In article <d53c8bc0-f649-46ca-b4c2-aae76770b...@w34g2000prm.googlegroups.com>, WC wrote: > Thanks for the reference.
> Where can I find a list of characters for all common groups? > [SO(n),E(n),U(n) etc]
Well, there are infinitely many irreducible representations of the simple or compact groups, (classified by Cartan's theorem of the highest weight)so I don't think you want to have a list of them all.
Weyl's Character formula gives a formula for the character in terms of the Weyl group and the highest weight. Also, it is known that the characters of the general linear group are symmetric functions (Schur functions etc, see MacDonalds book Symmetric Functions and Hall polynomials)).
If you want to see the characters of the finite simple groups there is the monumental Atlas of Finite Groups by Conway et al.
On May 14, 8:45Êam, WC <cacher.in.the....@gmail.com> wrote:
> What is the relation between characters of a group and its subgroup?
> e.g. what is the relation between characters of E(8) [group] and E(7) > and SU(2) [Sub-groups]?
This is an important and hard problem of the representation theory, known as "Branching rule". Many cases are solved for example for many classes of classical groups.
