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In mathematics, the finite-dimensional rep … In mathematics, the finite-dimensional representations of the complex classical Lie groups , , , , ,can be constructed using the general representation theory of semisimple Lie algebras. The groups , , are indeed simple Lie groups, and their finite-dimensional representations coincide with those of their maximal compact subgroups, respectively , , . In the classification of simple Lie algebras, the corresponding algebras are However, since the complex classical Lie groups are linear groups, their representations are tensor representations. Each irreducible representation is labelled by a Young diagram, which encodes its structure and properties.hich encodes its structure and properties.
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In mathematics, the finite-dimensional rep … In mathematics, the finite-dimensional representations of the complex classical Lie groups , , , , ,can be constructed using the general representation theory of semisimple Lie algebras. The groups , , are indeed simple Lie groups, and their finite-dimensional representations coincide with those of their maximal compact subgroups, respectively , , . In the classification of simple Lie algebras, the corresponding algebras aree algebras, the corresponding algebras are
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