外尔特征标公式（Weyl's character formula) 描述紧李群不可约表示的特征标。其名来自证明者赫尔曼·外尔。

定义：群G的表示r的特征标为一函数 ，，其中Tr 为线性算子之迹。 （由彼得-外尔定理 可知紧李群的任何不可约表示都是有限维的；故迹之定义为线性代数中之定义。）

特征标 χ 记住了表示 r 本身的重要消息。 外尔特征标公式用群G的其他数据来表达 χ 。 本文考虑复表示，不失一般亦设其为酉表示，因而「不可约」亦等价于「不可分解」（即非二子表示之直和）。

In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights. It was proved by HermannWeyl (1925, 1926a, 1926b).

By definition, the character of a representation r of G is the trace of r(g), as a function of a group element g in G. The irreducible representations in this case are all finite-dimensional (this is part of the Peter–Weyl theorem); so the notion of trace is the usual one from linear algebra. Knowledge of the character χ of r is a good substitute for r itself, and can have algorithmic content. Weyl's formula is a closed formula for the χ, in terms of other objects constructed from G and its Lie algebra. The representations in question here are complex, and so without loss of generality are unitary representations; irreducible therefore means the same as indecomposable, i.e. not a direct sum of two subrepresentations.