Lie Groups pp 112-116 | Cite as

The Weyl Integration Formula

  • Daniel Bump
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 (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.

Keywords

Conjugacy Class Weyl Group Haar Measure Maximal Torus Compact Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

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

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