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Lectures on Lie Algebras

In: Representation Theory, Complex Analysis, and Integral Geometry

Author

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  • Joseph Bernstein

    (Tel-Aviv University, Department of Mathematics)

Abstract

This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.

Suggested Citation

  • Joseph Bernstein, 2012. "Lectures on Lie Algebras," Springer Books, in: Bernhard Krötz & Omer Offen & Eitan Sayag (ed.), Representation Theory, Complex Analysis, and Integral Geometry, pages 97-132, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4817-6_6
    DOI: 10.1007/978-0-8176-4817-6_6
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