0
$\begingroup$

I have a set of permutation matrices (n x n) of a graph which form a group (the automorphisms). They are obviously a subgroup of the symmetric group S_n. Is there a way to find the irreducible representations of this group of matrices or, probably just as good, the characters of the irreducible representations?

I am new to this area of group theory (the symmetric group and subgroups) although I know about other finite groups used in the crystallographic symmetry groups along with the usual Schur's lemma, great orthogonality theorem, etc.

Any help or pointers greatly appreciated.

Thanks.

Improve this question
$\endgroup$
4
  • $\begingroup$ This has been discussed on MO a while ago. Searching with Google should unearth useful information. $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Aug 3, 2012 at 15:28
  • $\begingroup$ A standard strategy is to find subgroups or quotient groups whose representations you understand and induct or restrict their representations. See, for example, en.wikipedia.org/wiki/… . $\endgroup$
    – Qiaochu Yuan
    Commented Aug 3, 2012 at 17:20
  • 3
    $\begingroup$ Every finite group is a subgroup of some symmetric group. Without further information, you are simply asking how to compute the irreducible representation of some given finite group. Have a look at one of the standard books on character theory, such as Serre, or Isaacs. $\endgroup$
    – Alex B.
    Commented Aug 3, 2012 at 21:27
  • $\begingroup$ As Mariano said, check mathoverflow.net/questions/86019/…. For particular examples, you can use GAP function IrreducibleRepreentations. $\endgroup$
    – Leandro Vendramin
    Commented Aug 4, 2012 at 12:27

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .