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Find the decomposition of the standard two-dimensional rotation

  1. Apr 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the decomposition of the standard two-dimensional rotation representation of the cyclic group Cn by rotations into irreducible representations



    3. The attempt at a solution

    Ok i did this directly, finding complementary 1-dimensional G-invariant subspaces. but our teacher said we specifically need to do this using characters, which i have no clue how to do.
     
  2. jcsd
  3. Apr 29, 2009 #2

    matt grime

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    Re: Characters

    Write down the character of C_n acting by rotations on the plane. Find its inner product with the irreducible 1-d reps.
     
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