Induced character
Open-knowledge reference entry
In mathematics, an induced character is the character of the representation V of a finite group G induced from a representation W of a subgroup H ≤ G. More generally, there is also a notion of the induction of a class function f on H,
Ind
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f
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{\displaystyle \operatorname {Ind} (f)}
, given by the formula
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=
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∑
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{\displaystyle \operatorname {Ind} (f)(s)={\frac {1}{|H|}}\sum _{t\in G,\ t^{-1}st\in H}f(t^{-1}st).}
If f is a character of the representation W of H, then this formula for
Ind
(
f
)
{\displaystyle \operatorname {Ind} (f)}
calculates the character of the induced representation V of G.
The basic result on induced characters is Brauer's theorem on induced characters. It states that every irreducible character on G is a linear combination with integer coefficients of characters induced from elementary subgroups.
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