Representations of finite groups: Irreducible and reducible

  • #1
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Main Question or Discussion Point

Matrix representation of a finite group G is irreducible representation if
[tex]\sum^n_{i=1}|\chi_i|^2=|G|[/tex].
Representation is reducible if
[tex]\sum^n_{i=1}|\chi_i|^2>|G|[/tex].
What if
[tex]\sum^n_{i=1}|\chi_i|^2<|G|[/tex].
Are then multiplication of matrices form a group? If yes what we can say from ##\sum^n_{i=1}|\chi_i|^2<|G|##. ##\chi_i## are characters (traces of matrices).
 

Answers and Replies

  • #2
Orodruin
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You cannot have that situation.
 

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