Lossless-Join Decomposition

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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 HG. More generally, there is also a notion of induction Ind(f) of a class function f on H given by the formula

Ind(f)(s)=1|H|tG,t1stHf(t1st).

If f is a character of the representation W of H, then this formula for Ind(f) calculates the character of the induced representation V of G.[1]

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.

References

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