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Let be a group homomorphism, a representation of , and the character of . The induced character of is the character of the induced -representation
There is a formula for the induced character:
where the sum is over all pairs such that .
This formula is usually given only in the case when is injective, when it can be re-expressed as a sum over cosets. The case when is surjective is Exercise 7.1 of (Serre) and the general case is easy to put together from these. It can also be derived abstractly using bicategorical trace.
J-P. Serre, Linear Representations of Finite Groups
MO question about the non-injective case.
Last revised on March 1, 2012 at 22:10:25. See the history of this page for a list of all contributions to it.