Lectures on Lie algebras

Joseph Bernstein*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationRepresentation Theory, Complex Analysis, and Integral Geometry
PublisherBirkhauser Boston
Number of pages36
ISBN (Electronic)9780817648176
ISBN (Print)081764816X, 9780817648169
StatePublished - 1 Nov 2013


  • Harish-Chandra center
  • Kostant multiplicity formula
  • Lie algebra
  • Verma module
  • Weyl character formula


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