Abstract
By studying the L2 fonctions on a compact Lie group G, the Peter-Weyl Theorem gives a simultaneous construction of all irreducible representations of G. Two important problems remain. The first is to parametrize Ĝ in a reasonable manner and the second is to individually construct each irreducible representation in a natural way. The solution to both of these problems is closely tied to the notion of highest weights.
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(2007). Highest Weight Theory. In: Sepanski, M.R. (eds) Compact Lie Groups. Graduate Texts in Mathematics, vol 235. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49158-5_7
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DOI: https://doi.org/10.1007/978-0-387-49158-5_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-30263-8
Online ISBN: 978-0-387-49158-5
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