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Character, Multiplicity, and Decomposition Problems in the Representation Theory of Complex Lie Algebras

  • Peter FiebigEmail author
Chapter
Part of the UNIPA Springer Series book series (USS)

Abstract

This essay is meant as an introduction to a very successful approach towards understanding the structure of certain highest weight categories appearing in algebraic Lie theory. For simplicity, the focus lies on the case of the category \(\mathcal{O}\) of representations of a simple complex Lie algebra. We show how the approach yields a proof of the classical Kazhdan–Lusztig conjectures that avoids the theory of D-modules on flag varieties.

Notes

Acknowledgements

The author was partially supported by the DFG grant SP1388.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department MathematikFAU Erlangen–NürnbergErlangenGermany

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