Difference between revisions of "Irreducible linear representation"

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(Relation with other properties)
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==Relation with other properties==
 
==Relation with other properties==
  
 +
===Stronger properties===
 +
 +
* [[Minimally irreducible linear representation]]
 
===Weaker properties===
 
===Weaker properties===
  
 
* [[Completely reducible linear representation]]
 
* [[Completely reducible linear representation]]
 
* [[Indecomposable linear representation]]
 
* [[Indecomposable linear representation]]
 +
* [[Multiplicity-free linear representation]]
 
* [[Isotypical linear representation]]
 
* [[Isotypical linear representation]]

Revision as of 22:11, 15 September 2007

This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field


This article gives a basic definition in the following area: linear representation theory
View other basic definitions in linear representation theory |View terms related to linear representation theory |View facts related to linear representation theory

Definition

Symbol-free definition

A linear representation of a group is said to be irreducible if there is no proper nonzero invariant subspace for it.

Relation with other properties

Stronger properties

Weaker properties