| Information | |
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| has gloss | eng: 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. |
| lexicalization | eng: fundamental representation |
| instance of | e/Lie group |
| Meaning | |
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| French | |
| has gloss | fra: La représentation dun groupe de Lie ou dun algèbre de Lie est appelée représentation fondamentale si elle est irréductible, et que son poids le plus haut est un poids fondamental. |
| lexicalization | fra: Representation fondamentale |
| lexicalization | fra: Représentation fondamentale |
| Russian | |
| has gloss | rus: Фундаментальное представление — представление полупростой группы Ли или алгебры Ли, старший вес которого является фундаментальным весом. |
| lexicalization | rus: Фундаментальное представление |
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