Abstract
In this chapter, we follow Hermann Weyl’s original approach to establishing the Weyl character formula and the theorem of the highest weight.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Axler, S.: Linear Algebra Done Right, 2nd edn. Undergraduate Texts in Mathematics. Springer, New York (1997)
Baez, J.C.: The octonions. Bull. Am. Math. Soc. (N.S.) 39, 145–205 (2002); errata Bull. Am. Math. Soc. (N.S.) 42, 213 (2005)
Baldoni, M.W., Beck, M., Cochet, C., Vergne, M.: Volume computation for polytopes and partition functions for classical root systems. Discret. Comput. Geom. 35, 551–595 (2006)
Bonfiglioli, A., Fulci, R.: Topics in Noncommutative Algebra: The Theorem of Campbell, Baker, Hausdorff and Dynkin. Springer, Berlin (2012)
Bröcker, T., tom Dieck, T.: Representations of Compact Lie Groups. Graduate Texts in Mathematics, vol. 98. Springer, New York (1985)
Cagliero, L., Tirao, P.: A closed formula for weight multiplicities of representations of \(\mathrm{Sp}_{2}(\mathbb{C})\). Manuscripta Math. 115, 417–426 (2004)
Capparelli, S.: Computation of the Kostant partition function. (Italian) Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 6(8), 89–110 (2003)
Duistermaat, J., Kolk, J.: Lie Groups. Universitext. Springer, New York (2000)
Gotô, M.: Faithful representations of Lie groups II. Nagoya Math. J. 1, 91–107 (1950)
Hall, B.C.: Quantum Theory for Mathematicians. Graduate Texts in Mathematics, vol. 267. Springer, New York (2013)
Hassani, S.: Mathematical Physics: A Modern Introduction to its Foundations, 2nd edn. Springer, Heidelberg (2013)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002). A free (and legal!) electronic version of the text is available from the author’s web page at www.math.cornell.edu/~hatcher/AT/AT.pdf
Hoffman, K., Kunze, R.: Linear Algebra, 2nd edn. Prentice-Hall, Englewood Cliffs (1971)
Humphreys, J.: Introduction to Lie Algebras and Representation Theory. Second printing, revised. Graduate Texts in Mathematics, vol. 9. Springer, New York/Berlin (1978)
Jacobson, N.: Exceptional Lie Algebras. Lecture Notes in Pure and Applied Mathematics, vol. 1. Marcel Dekker, New York (1971)
Knapp, A.W.: Lie Groups Beyond an Introduction, 2nd edn. Progress in Mathematics, vol. 140. Birkhäuser, Boston (2002)
Knapp, A.W.: Advanced Real Analysis. Birkhäuser, Boston (2005)
Lee, J.: Introduction to Smooth Manifolds. 2nd edn. Graduate Texts in Mathematics, vol. 218. Springer, New York (2013)
Miller, W.: Symmetry Groups and Their Applications. Academic, New York (1972)
Poincaré, H.: Sur les groupes continus. Comptes rendus de l’Acad. des Sciences 128, 1065–1069 (1899)
Poincaré, H.: Sur les groupes continus. Camb. Philos. Trans. 18, 220–255 (1900)
Pugh, C.C.: Real Mathematical Analysis. Springer, New York (2010)
Rossmann, W.: Lie Groups. An Introduction Through Linear Groups. Oxford Graduate Texts in Mathematics, vol. 5. Oxford University Press, Oxford (2002)
Rudin, W.: Principles of Mathematical Analysis, 3rd edn. International Series in Pure and Applied Mathematics. McGraw-Hill, New York-Auckland-Düsseldorf (1976)
Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill, New York (1987)
Runde, V.: A Taste of Topology. Universitext. Springer, New York (2008)
Tarski, J.: Partition function for certain Simple Lie Algebras. J. Math. Phys. 4, 569–574 (1963)
Tuynman, G.M.: The derivation of the exponential map of matrices. Am. Math. Mon. 102, 818–819 (1995)
Varadarajan, V.S.: Lie Groups, Lie Algebras, and Their Representations. Reprint of the 1974 edn. Graduate Texts in Mathematics, vol. 102. Springer, New York (1984)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hall, B. (2015). The Compact Group Approach to Representation Theory. 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_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-13467-3_12
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)