Finding irreducible representations for C2, C3 and C3v groups

[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.

 

[Don Aman]

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?

Find M first. The eigenspaces will be the irreducible reps

 

[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?

 

[Don Aman]

Presuming you mean over R ro C or even Q.

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

 

[matt grime]

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