Homework question regarding irreducible representations

PhysKid24
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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.
 
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PhysKid24 said:
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
 
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?
 
matt grime said:
Presuming you mean over R ro C or even Q.
I think any field of characteristic other than 2 will work.
 
it even works with char 2. there is one simple rep in char 2, this gives it twice.
 

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