The Weyl Integration Formula
Let G be a compact, connected Lie group, and let T be a maximal torus. Theorem 16.5 implies that every conjugacy class meets T. Thus, we should be able to compute the Haar integral of a class function (for example, the inner product of two characters) as an integral over the torus. The formula that allows this, the Weyl Integration Formula, is therefore fundamental in representation theory and in other areas, such as random matrix theory.
KeywordsConjugacy Class Weyl Group Haar Measure Maximal Torus Compact Subgroup
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