Abstract
In this chapter, we study the finite-dimensional irreducible representations of sl(2, C). In doing this, we shall see, in a stripped-down form, many of the ideas needed to study representations of an arbitrary semisimple Lie algebra. Later we will see that representations of sl(2, C) control a large part of the structure of all semisimple Lie algebras.
We shall use the basis of sl(2, C) introduced in Exercise 1.12 throughout this chapter. Recall that we set
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© 2006 Springer-Verlag London Limited
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Erdmann, K., Wildon, M.J. (2006). Representations of sl(2, C). In: Introduction to Lie Algebras. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/1-84628-490-2_8
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DOI: https://doi.org/10.1007/1-84628-490-2_8
Publisher Name: Springer, London
Print ISBN: 978-1-84628-040-5
Online ISBN: 978-1-84628-490-8
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