Irreducible representation of dihedral group : D_n over C (complex)
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Let D_n be the dihedral group. Classify the irreducible representations of D_n over C (complex).
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Solution Summary
Irreducible representation of a dihedral group are classified. The solution is detailed.
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Some notation:
leq means less or equal;
^ = to the power
_ = 'sub'
neq = not equal to
the number of complex irreps correspond exactly to the number of conjugacy classes.
let G = D_{2n}, where n is odd; the usual presentation is <a,b: a^n = b^2 = 1, b^{-1}ab = a^{-}>
first consider a^i for 1 leq i leq n-1. Since the centralizer C(a^i) (in G!) contains <a>, the index of the centralizer is at most 2
|G:C(a^i)| leq |G: <a>| ...
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