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Character of a Hom representation

For complex representations

V, W

of a finite group,

Hom_{C} (V, W) ≅ V^{*} \otimes W .

Under the

G \times G

action

(g, h) α = σ (h) α ρ (g^{- 1})

, its character is

χ_{Hom (V, W)} (g, h) = \overline{χ_{V} (g)} χ_{W} (h) .

Table of contents 81 1
- Two-sided regular representation decomposition Character of a Hom representation 57

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