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Find the decomposition of the standard two-dimensional rotation

  • #1

Homework Statement



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



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.
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
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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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