Real character of a linear representation: Difference between revisions
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==Definition== | ==Definition== | ||
Let <math>G</math> be a group. A [[character of a linear representation|character]] <math>\chi</math> of a complex [[linear representation]] of <math>G</math> is called '''real''' if <math>\chi(g) \in \mathbb{R}</math> for every <math>g \in G</math>. | Let <math>G</math> be a group. A [[character of a linear representation|character]] <math>\chi</math> of a complex [[linear representation]] of <math>G</math> is called '''real''' if <math>\chi(g) \in \mathbb{R}</math> for every <math>g \in G</math>. Equivalently, <math>\chi(g) = \overline{\chi(g)}</math> for every <math>g \in G</math>. | ||
==Facts== | |||
* [[Number of real conjugacy classes is equal to number of irreducible real characters]] | |||
Latest revision as of 19:29, 7 November 2023
This term makes sense in the context of a linear representation of a group, viz an action of the group as linear automorphisms of a vector space
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
Let be a group. A character of a complex linear representation of is called real if for every . Equivalently, for every .
