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 (e.g., 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.
- 61.P. Halmos. Measure Theory. D. Van Nostrand Company, Inc., New York, N. Y., 1950.Google Scholar
- 69.E. Hewitt and K. Ross. Abstract Harmonic Analysis. Vol. I, Structure of topological groups, integration theory, group representations, volume 115 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition, 1979.Google Scholar