Linear representation theory: Difference between revisions
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The following is a list of useful results in linear representation theory: | The following is a list of useful results in linear representation theory: | ||
===Important theorems=== | |||
* [[Maschke's theorem]] | * [[Maschke's theorem]] | ||
* [[Schur's lemma]] | * [[Schur's lemma]] | ||
* [[Character orthogonality theorem]] | * [[Character orthogonality theorem]] | ||
===Other important results=== | |||
* [[Irreducible complex representation of abelian group is one dimensional]] | |||
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Revision as of 20:51, 30 October 2023
The linear representation theory of groups (or representation theory or group representation theory) is the study of linear representations of groups. A linear representation of a group over a field is a homomorphism where is a vector space over and denotes the general linear group of , viz the group of automorphisms of as a -vector space.
Important definitions
Further information: Basic definitions in linear representation theory
- linear representation
- subrepresentation
- irreducible linear representation
- completely reducible linear representation
- character
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Results
The following is a list of useful results in linear representation theory:
Important theorems
Other important results
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Applications
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