chapter  16
10 Pages

Reducible Characters

WithVictor E. Hill, Thomas T. Read

By Maschke’s theorem (12.10), every complex representation of a finite group G is completely reducible. If T is any complex representation of G and if χ is the character associated with T, then T is equivalent to a representation of the form: [ T 1 ( g ) T 2 ( g ) 0 ⋱ 0 T r ( g ) ]