# Regular Representation

1. Mar 27, 2005

### PhysKid24

Hi,

I have a question regarding group theory. For the cyclic group C2 with elements e and a, what are the matrices of the regular representation? How do you find this? How would I reduce this representation into irreducible representation? Lastly, how do I find a matrix which brings the regualr representation into block diagonal form? Thanks.

Last edited: Mar 27, 2005
2. Mar 28, 2005

### matt grime

At last, some representation theory to do (my area).

The regular rep is two dimesional, saw with basis e and f corresponding to 1 and g in G resp.

1 is sent to the identity, natch, and g sends e to f and f to e, so it is the matrix

$$\left( \begin{array}{cc}0&1\\1&0\end{array} \right)$$

i'm sure i can leave you to diagonalize that, over R or C (but not a field of characteristic 2).