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(All groups in the following discussion are assumed to be finite.)

Character induction is an operation that produces a character of a group given a character of a subgroup. I'm aware that there are other methods to get a character of a group from a given character of a subgroup, which aren't used as frequently as induction is (e.g. tensor induction, Suzuki's theory of exceptional characters).

Questions:

  1. Has any attempt been made to formalize the notion of "deriving a character of a group from a given character of a subgroup"?

  2. What are some other ways to get new characters from given characters?

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    $\begingroup$ For 2: surely tensor product deserves to be mentioned. $\endgroup$
    – Sam Hopkins
    Commented Aug 6, 2023 at 23:38
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    $\begingroup$ Related: mathoverflow.net/a/448813/123673 $\endgroup$
    – Kenta Suzuki
    Commented Aug 7, 2023 at 0:00
  • $\begingroup$ Do supercharacters count? $\endgroup$
    – Timothy Chow
    Commented Aug 7, 2023 at 19:34
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    $\begingroup$ It's often easy to modify characters of a given finite group $G$ to obtain new generalized characters ( using Brauer's characterization of characters, for example). However, showing when the resulting functions are actually characters is often difficult. $\endgroup$
    – Geoff Robinson
    Commented Aug 11, 2023 at 9:01

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