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Lie Groups pp 123-128 | Cite as

The Weyl Integration Formula

  • Daniel Bump
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

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.

References

  1. 61.
    P. Halmos. Measure Theory. D. Van Nostrand Company, Inc., New York, N. Y., 1950.Google Scholar
  2. 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

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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