Definitions
Let V be a finite-dimensional vector space over a field F and let ρ: G → GL(V) be a representation of a group G on V. The character of ρ is the function χρ: G → F given by
where Tr is the trace.
A character χρ is called irreducible if ρ is an irreducible representation. It is called linear if the dimension of ρ is 1. When G is finite and F has characteristic zero, the kernel of the character χρ is the normal subgroup:, which is precisely the kernel of the representation ρ.
Read more about this topic: Character Theory
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