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Highest weight (lie algebras)

  1. Dec 29, 2007 #1
    I know that the highest weight of an irreducible representation is unique (up to scaling). Is the converse true, however? I have seen some proofs of the irreducibility of certain representations that proceed by showing the uniqueness of the highest weight. How do we know that this is a valid approach?
     
  2. jcsd
  3. Dec 30, 2007 #2

    CompuChip

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    By: "the converse", you mean: If the highest weight of a representation is unique, it is irreducible?
     
  4. Dec 30, 2007 #3
    Yes.
     
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