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About: Induced representation

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In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations.

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  • Im mathematischen Gebiet der Darstellungstheorie von Gruppen kann man mittels der induzierten Darstellung aus einer Darstellung einer Untergruppe eine Darstellung der sie enthaltenden Gruppe konstruieren. (de)
  • In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations. Induced representations were initially defined by Frobenius, for linear representations of finite groups. The idea is by no means limited to the case of finite groups, but the theory in that case is particularly well-behaved. (en)
  • En mathématiques une représentation induite est une représentation d'un groupe canoniquement associée à une représentation de l'un de ses sous-groupes. L'induction est adjointe à gauche de la (en). Cette propriété intervient dans la formule de réciprocité de Frobenius. Cet article traite le cas des groupes finis. (fr)
  • 군 표현론에서 유도 표현(誘導表現, 영어: induced representation)은 부분군의 표현을 전체 군의 표현으로 확장시키는 방법이다. (ko)
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  • Im mathematischen Gebiet der Darstellungstheorie von Gruppen kann man mittels der induzierten Darstellung aus einer Darstellung einer Untergruppe eine Darstellung der sie enthaltenden Gruppe konstruieren. (de)
  • En mathématiques une représentation induite est une représentation d'un groupe canoniquement associée à une représentation de l'un de ses sous-groupes. L'induction est adjointe à gauche de la (en). Cette propriété intervient dans la formule de réciprocité de Frobenius. Cet article traite le cas des groupes finis. (fr)
  • 군 표현론에서 유도 표현(誘導表現, 영어: induced representation)은 부분군의 표현을 전체 군의 표현으로 확장시키는 방법이다. (ko)
  • In group theory, the induced representation is a representation of a group, G, which is constructed using a known representation of a subgroup H. Given a representation of H, the induced representation is, in a sense, the "most general" representation of G that extends the given one. Since it is often easier to find representations of the smaller group H than of G, the operation of forming induced representations is an important tool to construct new representations. (en)
rdfs:label
  • Induzierte Darstellung (de)
  • Représentation induite d'un groupe fini (fr)
  • Induced representation (en)
  • 유도 표현 (ko)
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