Abstract
The representation theory of finite groups is a subject going back to the late eighteen hundreds. The pioneers in the subject were G. Frobenius, I. Schur, and W. Burnside. Modern approaches tend to make heavy use of module theory and the Wedderburn theory of semisimple algebras. But the original approach, which nowadays can be thought of as via discrete Fourier analysis, is much more easily accessible and can be presented, for instance, in an undergraduate course. The aim of this text is to exposit the essential ingredients of the representation theory of finite groups over the complex numbers assuming only knowledge of linear algebra and undergraduate group theory, and perhaps a minimal familiarity with ring theory.
Keywords
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.
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 subscriptionsAuthor information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Steinberg, B. (2012). Introduction. In: Representation Theory of Finite Groups. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0776-8_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0776-8_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0775-1
Online ISBN: 978-1-4614-0776-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)