Abstract
Dirac operators were introduced into representation theory by Parthasarathy [Par] as a tool to construct the discrete series representations. The final results, which applied to all discrete series, were obtained by Atiyah and Schmid in [AS]. In this chapter we study an algebraic version of Parthasarathy’s Dirac operator, due to Vogan. In particular, we explain the notion of Dirac cohomology of Harish-Chandra modules, and Vogan’s conjecture which predicts the infinitesimal character of modules with nonzero Dirac cohomology [V3]. We present a proof of this conjecture following [HP1].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2006 Birkhäuser Boston
About this chapter
Cite this chapter
(2006). Dirac Operators in the Algebraic Setting. In: Dirac Operators in Representation Theory. Mathematics: Theory & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4493-2_3
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4493-2_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3218-2
Online ISBN: 978-0-8176-4493-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)