In mathematics, a Young symmetrizer is an element of the group algebra of the symmetric group S n {\displaystyle S_{n}} whose natural action on tensor products V ⊗ n {\displaystyle V^{\otimes n}} of a complex vector space V {\displaystyle V} has as image an irreducible representation of the group of invertible linear transformations G L ( V ) {\displaystyle GL(V)} . All irreducible representations of G L ( V ) {\displaystyle GL(V)} are thus obtained.
In mathematics, a Young symmetrizer is an element of the group algebra of the symmetric group S n {\displaystyle S_{n}} whose natural action on tensor products V ⊗ n {\displaystyle V^{\otimes n}} of a complex vector space V {\displaystyle V} has as image an irreducible representation of the group of invertible linear transformations G L ( V ) {\displaystyle GL(V)} . All irreducible representations of G L ( V ) {\displaystyle GL(V)} are thus obtained.
Source: Wikipedia "Young symmetrizer" · CC BY-SA 4.0
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