Induced Representation
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📖Definition
Constructing representation of group from representation of subgroup
📐Formulas
Ind_H^G V = ℂ[G] ⊗_ℂ[H] V
Frobenius reciprocity: ⟨Ind V, W⟩_G = ⟨V, Res W⟩_H
dim Ind V = [G:H] dim V
✏️Examples
예제 1
Inducing from cyclic to symmetric
예제 2
Regular rep = Ind_1^G 1
⚡Applications
Representation construction
Mackey theory
Analytic number theory
🔗Related Documents
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