Young symmetrizer

noun

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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Meanings

nounYoung symmetrizer (plural Young symmetrizers)

plural Young symmetrizers

  1. mathematicsAn 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.

Origin

Named after British mathematician Alfred Young.

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Cite this entry
APA

Young symmetrizer. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Young%20symmetrizer

MLA

“Young symmetrizer.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Young%20symmetrizer. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Young symmetrizer,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Young%20symmetrizer.

Source: Young symmetrizer on Wiktionary, CC BY-SA 4.0.