"Young symmetrizer" meaning in English

{
  "etymology_text": "Named after British mathematician Alfred Young.",
  "forms": [
    {
      "form": "Young symmetrizers",
      "tags": [
        "plural"
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      "expansion": "Young symmetrizer (plural Young symmetrizers)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "glosses": [
        "An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers."
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          "group algebra",
          "group ring"
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        [
          "symmetric group",
          "symmetric group"
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          "homomorphism"
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          "endomorphism",
          "endomorphism"
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          "vector space",
          "vector space"
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        [
          "permutation",
          "permutation"
        ],
        [
          "indices",
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          "image"
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          "irreducible"
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          "complex number",
          "complex number"
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      "raw_glosses": [
        "(mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers."
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        "Young symmetrizer"
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  "word": "Young symmetrizer"
}

{
  "etymology_text": "Named after British mathematician Alfred Young.",
  "forms": [
    {
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      "tags": [
        "plural"
      ]
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      "glosses": [
        "An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers."
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      "raw_glosses": [
        "(mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers."
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}