Abstract
In this chapter we want to have a first look into the representation theory of various groups with extra structure, such as algebraic or compact groups. We will use the necessary techniques from elementary algebraic geometry or functional analysis, referring to standard textbooks. One of the main points is a very tight relationship between a special class of algebraic groups, the reductive groups, and compact Lie groups. We plan to illustrate this in the classical examples, leaving the general theory to Chapter 10.
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© 2007 Springer Science+Business Media, LLC
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(2007). Group Representations. In: Lie Groups. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-0-387-28929-8_8
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DOI: https://doi.org/10.1007/978-0-387-28929-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-26040-2
Online ISBN: 978-0-387-28929-8
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