Homework question regarding irreducible representations

1. Apr 12, 2005

PhysKid24

Hi,

I keep having problems with a homework question regarding irreducible representations. For the C2 group,which has only two elements,say, e and a, Iwas able to find the regular representations for them, yet i don't know how to find an irreducible representation for them. I'm also supposed to find a matrix M which diagonalizes D(reg)? Do I find M first and then the irreducible representation?Can anyone help?? I'm also to do the same procedure for group C3 and C3v. Thanks.

2. Apr 12, 2005

Don Aman

Find M first. The eigenspaces will be the irreducible reps

3. Apr 12, 2005

matt grime

Presuming you mean over R ro C or even Q.
what about the map sending a to 1, and the map sending a to -1 in any of these spaces?

4. Apr 12, 2005

Don Aman

I think any field of characteristic other than 2 will work.

5. Apr 13, 2005

matt grime

it even works with char 2. there is one simple rep in char 2, this gives it twice.