Irreducible character of a linear representation

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
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Definition

A character of a linear representation is called irreducible if its corresponding representation is an irreducible representation.

Results

• An incredibly useful result is that the sum of the squares of the degrees of all irreducible characters of a group is equal to the order of that group, see sum of squares of degrees of irreducible representations equals order of group.
• An incredibly useful theorem is also the character orthogonality theorem, of which the above is a special case.
• Representation is irreducible if and only if inner product of character is 1