Abstract
In this chapter we review the basic properties of the (g, K)-modules obtained by cohomological induction. These properties are roughly as follows: let Z be an (g, L ⋂ K)-module with infinitesimal character λ. Then the cohomologically induced modules have g-infinitesimal character λ + ρ(u), where ρ(u) is the half sum of roots corresponding to u. Under appropriate dominance conditions, they are:
-
•
nonzero only in the middle degree S, and moreover RS (Z) ≔ Ls(Z);
-
•
irreducible if Z is irreducible;
-
•
unitary if Z is unitary.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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). Properties of Cohomologically Induced Modules. In: Dirac Operators in Representation Theory. Mathematics: Theory & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4493-2_6
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4493-2_6
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)