Weight space is a concept in representation theory that refers to the decomposition of a representation of a Lie algebra or Lie group into eigenspaces associated with weights. Each weight corresponds to a character of a one-dimensional representation, and the weight space is spanned by eigenvectors that share the same eigenvalue. This framework is crucial for understanding how representations are structured, especially in semisimple Lie algebras, where weight spaces organize the representations into manageable components.
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