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Regular Representation

  1. Mar 27, 2005 #1
    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. jcsd
  3. Mar 28, 2005 #2

    matt grime

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    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

    [tex]\left( \begin{array}{cc}0&1\\1&0\end{array} \right) [/tex]

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