Centre of a character

Let $𝔛 : 𝐺 \to 𝖵 𝖾 𝖼 𝗍 (ℂ)$ be a finite-degree representation affording character $𝜒$ . Then

| 𝜒 (𝑔) | = 𝜒 (1) ⟺ 𝔛 (𝑔) = 𝜆 1

for some $𝜆 \in ℂ$ . rep

Proof

proof