character (character theory) Character theory is an important tool in the study of finite groups. The character χφ:G → F of a representation φ:G → GL(V) is the map χφ(g) = traceφ(g). Here G is a group and V is a finite-dimensional vector space over a field F. The degree of the character is the dimension of V. A character is called irreducible if the representation is irreducible. See character table.
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