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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bump, D. (2004). The Weyl Integration Formula. In: Lie Groups. Graduate Texts in Mathematics, vol 225. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4094-3_18
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4094-3_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1937-3
Online ISBN: 978-1-4757-4094-3
eBook Packages: Springer Book Archive