Editing Fundamental representation (section)

In [[representation theory]] of [[Lie group]]s and [[Lie algebra]]s, a '''fundamental representation''' is an [[irreducible representation|irreducible finite-dimensional representation]] of a [[semisimple Lie algebra|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.