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In mathematics, the Schur orthogonality relations, which were proven by Issai Schur through Schur's lemma, express a central fact about representations of finite groups. They admit a generalization to the case of compact groups in general, and in particular compact Lie groups, such as the rotation group SO(3).

Attributes	Values
rdfs:label	Orthogonalitätsrelationen (de) 大直交性定理 (ja) 슈어 직교 관계 (ko) Schur orthogonality relations (en) 舒尔正交关系 (zh)
rdfs:comment	Im mathematischen Teilgebiet der Gruppentheorie sind die Orthogonalitätsrelationen bestimmte Beziehungen zwischen Charakteren von Darstellungen einer Gruppe. Der Name rührt daher, dass man auf einem geeigneten Funktionenraum, der die Charaktere enthält, ein inneres Produkt definieren kann, bzgl. dessen verschiedene Charaktere tatsächlich orthogonal sind. (de) In mathematics, the Schur orthogonality relations, which were proven by Issai Schur through Schur's lemma, express a central fact about representations of finite groups. They admit a generalization to the case of compact groups in general, and in particular compact Lie groups, such as the rotation group SO(3). (en) 군 표현론에서 슈어 직교 관계(Schur直交關係, 영어: Schur orthogonality relation)는 유한군이나 보다 일반적으로 콤팩트 위상군에서 성립하는, 표현들의 성분 또는 사이의 일련의 직교 관계에 대한 정리이다. (ko) 位数g (元の数)の群G の既約表現α のユニタリー表現行列D(α) の行列要素をD(α)ij(G)と書くと、その間には以下の直交関係がある。ここで和記号はGのすべての元についての和を意味する。dαは表現行列の次元である。これを表現行列についての大直交性定理と呼ぶ。大直交性定理はシューアの補題から導かれる。 (ja) 舒尔正交关系（英語：Schur orthogonality relations）描述了有限群表示中的核心事实。它可以推广到一般的紧群，特别是紧李群，比如旋转群 SO(3)。此關係可藉由舒尔引理證明。 (zh)
dcterms:subject	Representation theory of groups
Wikipage page ID	7947411 (xsd:integer)
Wikipage revision ID	1038463540 (xsd:integer)
Link from a Wikipage to another Wikipage	Matrix (mathematics) Compact group Orthonormal basis Matrix coefficient Trace (linear algebra) Wigner D-matrix Haar measure Irreducible representation Group (mathematics) Representation theory of groups Issai Schur Character theory Rotation group SO(3) Class function Group representation Inner product space Kronecker delta Young tableau Schur's lemma Unitary representation Symmetric group Point groups in three dimensions Peter–Weyl theorem Centralizer
Link from a Wikipage to an external page	https://archive.org/details/linearrepresenta1977serr/page/13 https://archive.org/details/linearrepresenta1977serr/page/13%7Ctitle=Linear https://www.springer.com/gp/book/9781461412304%7Ctitle=Representing
sameAs	Schur orthogonality relations Schur orthogonality relations Schur orthogonality relations Schur orthogonality relations Schur orthogonality relations Schur orthogonality relations Schur orthogonality relations
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Math dbt:Mvar dbt:Reflist
has abstract	Im mathematischen Teilgebiet der Gruppentheorie sind die Orthogonalitätsrelationen bestimmte Beziehungen zwischen Charakteren von Darstellungen einer Gruppe. Der Name rührt daher, dass man auf einem geeigneten Funktionenraum, der die Charaktere enthält, ein inneres Produkt definieren kann, bzgl. dessen verschiedene Charaktere tatsächlich orthogonal sind. (de) In mathematics, the Schur orthogonality relations, which were proven by Issai Schur through Schur's lemma, express a central fact about representations of finite groups. They admit a generalization to the case of compact groups in general, and in particular compact Lie groups, such as the rotation group SO(3). (en) 군 표현론에서 슈어 직교 관계(Schur直交關係, 영어: Schur orthogonality relation)는 유한군이나 보다 일반적으로 콤팩트 위상군에서 성립하는, 표현들의 성분 또는 사이의 일련의 직교 관계에 대한 정리이다. (ko) 位数g (元の数)の群G の既約表現α のユニタリー表現行列D(α) の行列要素をD(α)ij(G)と書くと、その間には以下の直交関係がある。ここで和記号はGのすべての元についての和を意味する。dαは表現行列の次元である。これを表現行列についての大直交性定理と呼ぶ。大直交性定理はシューアの補題から導かれる。 (ja) 舒尔正交关系（英語：Schur orthogonality relations）描述了有限群表示中的核心事实。它可以推广到一般的紧群，特别是紧李群，比如旋转群 SO(3)。此關係可藉由舒尔引理證明。 (zh)
prov:wasDerivedFrom	wikipedia-en:Schur_orthogonality_relations?oldid=1038463540&ns=0
page length (characters) of wiki page	13886 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Schur_orthogonality_relations
is Link from a Wikipage to another Wikipage of	Maschke's theorem Glossary of representation theory Frobenius reciprocity Frobenius–Schur indicator Matrix coefficient Wigner D-matrix Representation theory of finite groups Issai Schur Burnside's theorem Great orthogonality theorem Schur orthogonality relation The great orthogonality theorem Schur's lemma List of things named after Issai Schur Semisimple representation Orthogonality theorem Grand orthogonality theorem Group orthogonality theorem
is Wikipage redirect of	Great orthogonality theorem Schur orthogonality relation The great orthogonality theorem Orthogonality theorem Grand orthogonality theorem Group orthogonality theorem
is foaf:primaryTopic of	wikipedia-en:Schur_orthogonality_relations

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