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How to prove that the symmetry group of a regular polygon has only 1 and 2 dim irredu

  1. Nov 20, 2009 #1
    how to prove that the symmetry group of a regular polygon has only 1 and 2 dim irreducible representations?
     
  2. jcsd
  3. Nov 24, 2009 #2

    morphism

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    Re: how to prove that the symmetry group of a regular polygon has only 1 and 2 dim ir

    The group in question, i.e. the dihedral group, has an abelian subgroup of index 2 (the one generated by the reflection). Thus any irreducible representation is at most 2 dimensional. I'll let you fill in the details. Post back if you need more help!
     
    Last edited: Nov 24, 2009
  4. Nov 25, 2009 #3
    Re: how to prove that the symmetry group of a regular polygon has only 1 and 2 dim ir

    Thanks a lot

    maybe you mean the rotation subgroup is of index 2?

    i will think of it.
     
  5. Nov 27, 2009 #4

    morphism

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    Re: how to prove that the symmetry group of a regular polygon has only 1 and 2 dim ir

    Yup - sorry! (The reflection subgroup has order 2!)
     
  6. Oct 25, 2010 #5
    Re: how to prove that the symmetry group of a regular polygon has only 1 and 2 dim ir

    but i still can not figure out the proof

    any hint?

    is there any theorem?
     
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