Dirac Operators in Representation Theory pp 115-132 | Cite as

# Properties of Cohomologically Induced Modules

Chapter

## 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 R^{S}(*Z*) ≔ L_{s}(*Z*); - •
irreducible if

*Z*is irreducible; - •
unitary if

*Z*is unitary.

## Keywords

Spectral Sequence Natural Isomorphism Cartan Subalgebra Adjoint Action Good Range
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.

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## Copyright information

© Birkhäuser Boston 2006