Abstract
In this lecture, we will illustrate the general paradigm of the previous lecture by applying it to the Lie algebras\(\mathfrak{s}{\mathfrak{l}_n}\mathbb{C}\) this is typical of the analyses of specific Lie algebras carried out in this Part. We start in §15.1 by describing the Cartan subalgebra, roots, root spaces, etc., for\(\mathfrak{s}{\mathfrak{l}_n}\mathbb{C}\)in general. We then give in §15.2 a detailed account of the representations of\(\mathfrak{s}{\mathfrak{l}_n}\mathbb{C}\), which generalizes directly to\(\mathfrak{s}{\mathfrak{l}_n}\mathbb{C}\)in particular, we deduce the existence part of Theorem 14.18 for \(\mathfrak{s}{{\mathfrak{l}}_{n}}\mathbb{C} \).
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© 2004 Springer Science+Business Media New York
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Fulton, W., Harris, J. (2004). sl4ℂ and slnℂ. In: Representation Theory. Graduate Texts in Mathematics, vol 129. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0979-9_15
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DOI: https://doi.org/10.1007/978-1-4612-0979-9_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-3-540-00539-1
Online ISBN: 978-1-4612-0979-9
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