Induced character explained

\operatorname{Ind}(f) of a class function f on H given by the formula\operatorname{Ind}(f)(s) = (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

\operatorname{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.

Notes and References

1. . Translated from the second French edition by Leonard L. Scott.