Class Field Theory
《Class Field Theory》 · 第 277 页 · Chapter 10，Section 10.4「The Weyl Character Formula」，Theorem 10.14
Theorem 10.14 (Weyl Character Formula). If $(\pi,V)$ is an irreducible representation of $\mathfrak g$ with highest weight $\Lambda$, then $\chi_\pi(H) = \frac{\sum_{w\in W} \det(w)e^{\langle w(\Lambda+\delta), H\rangle}}{\sum_{w\in W} \det(w)e^{\langle w\cdot\delta, H\rangle}}$ for all $H\in\mathfrak h$ for which the denominator is nonzero.