In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight. For example, the defining module of a classical Lie group is a fundamental representation. Any finite-dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to Élie Cartan. Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite-dimensional representations.
Read more about Fundamental Representation: Examples, Explanation, Other Uses
Famous quotes containing the word fundamental:
“Our species successfully raised children for tens of thousands of years before the first person wrote down the word “psychology.” The fundamental skills needed to be a parent are within us. All we’re really doing is fine-tuning a process that’s already remarkably successful.”
—Lawrence Kutner (20th century)