Abstract
In this chapter and Chapter 12 we develop the representation theory of a connected, compact matrix Lie group K. The main result is a “theorem of the highest weight,” which is very similar to our main results for semisimple Lie algebras.
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
References
Lee, J.: Introduction to Smooth Manifolds. 2nd edn. Graduate Texts in Mathematics, vol. 218. Springer, New York (2013)
Rudin, W.: Principles of Mathematical Analysis, 3rd edn. International Series in Pure and Applied Mathematics. McGraw-Hill, New York-Auckland-Düsseldorf (1976)
Hassani, S.: Mathematical Physics: A Modern Introduction to its Foundations, 2nd edn. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hall, B. (2015). Compact Lie Groups and Maximal Tori. In: Lie Groups, Lie Algebras, and Representations. Graduate Texts in Mathematics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-13467-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-13467-3_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13466-6
Online ISBN: 978-3-319-13467-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)