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DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-30
How statement and proof provenance work

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The induced character Ind⁡HGχ of a complex character

Definition

Let G be a finite group, let H≤G, and let W be a finite-dimensional complex representation of H with character χW (The character χV(g)=tr⁡(ρV(g)) of a finite-dimensional complex representation).

The induced character of χW is the character of the induced representation:

Ind⁡HGχW:=χInd⁡HGW.

When the representation affording χW is denoted simply by W, one also writes χInd⁡HGW.

Remarks

  • The notation depends only on the character, not on a chosen model of the representation: equivalent H-representations induce equivalent G-representations by postcomposing every induced function with the intertwiner.

  • The explicit value formula for Ind⁡HGχ is proved in Frobenius' formula for the character of an induced representation.

Depends on

Used by

Dependency tree · two levels

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Sources