Find the decomposition of the standard two-dimensional rotation

[SNOOTCHIEBOOCHEE]

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.

 

[matt grime]

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