About: Schur–Weyl duality

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Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups. It is named after two pioneers of representation theory of Lie groups, Issai Schur, who discovered the phenomenon, and Hermann Weyl, who popularized it in his books on quantum mechanics and classical groups as a way of classifying representations of unitary and general linear groups. Schur–Weyl duality can be proven using the double centralizer theorem.

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rdfs:label	Schur–Weyl duality (en)
rdfs:comment	Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups. It is named after two pioneers of representation theory of Lie groups, Issai Schur, who discovered the phenomenon, and Hermann Weyl, who popularized it in his books on quantum mechanics and classical groups as a way of classifying representations of unitary and general linear groups. Schur–Weyl duality can be proven using the double centralizer theorem. (en)
name	Lemma 1 (en) Lemma 2 (en)
dcterms:subject	Representation theory of groups Representation theory Tensors
Wikipage page ID	15291970 (xsd:integer)
Wikipage revision ID	1097584654 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum mechanics Roger Evans Howe Partition algebra Representation theory Double centralizer theorem Lie group Maschke's theorem Matrix multiplication General linear group Equivariant map Symmetry Classical groups Trivial representation Brauer algebra Regular representation Group action (mathematics) Hermann Weyl Representation theory of groups Issai Schur Tensor Representation theory Tensors Unitary group Symmetric group Finite group Semisimple representation Centralizer (ring theory) Young diagram dbr:Sign_representation
Link from a Wikipage to an external page	https://www.springer.com/gp/book/9781461412304%7Ctitle= https://mathoverflow.net/q/255492
sameAs	Schur–Weyl duality Schur–Weyl duality Schur–Weyl duality
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Math_theorem dbt:Fulton-Harris dbt:MR
has abstract	Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups. It is named after two pioneers of representation theory of Lie groups, Issai Schur, who discovered the phenomenon, and Hermann Weyl, who popularized it in his books on quantum mechanics and classical groups as a way of classifying representations of unitary and general linear groups. Schur–Weyl duality can be proven using the double centralizer theorem. (en)
math statement	If is a simple left A-module, then is a simple left B-module. (en) When and G is the symmetric group , a subspace of is a B-submodule if and only if it is invariant under ; in other words, a B-submodule is the same as a -submodule. (en)
gold:hypernym	Theorem
prov:wasDerivedFrom	wikipedia-en:Schur–Weyl_duality?oldid=1097584654&ns=0
page length (characters) of wiki page	9054 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Schur–Weyl_duality
is Link from a Wikipage to another Wikipage of	List of dualities Glossary of representation theory Michela Varagnolo Schur algebra Representation theory of the symmetric group Brauer algebra Capelli's identity Hermann Weyl Issai Schur The Classical Groups Hook length formula Tensor product of representations Young tableau List of things named after Hermann Weyl List of things named after Issai Schur Yangian Schur-Weyl duality
is Wikipage redirect of	Schur-Weyl duality
is foaf:primaryTopic of	wikipedia-en:Schur–Weyl_duality

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