wc

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]?

maarten bergvelt

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

wc

Thanks for the reference.

Where can I find a list of characters for all common groups?
[SO(n),E(n),U(n) etc]

WC

maarten bergvelt

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.


--
Maarten Bergvelt

shahryari

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.