Properties of Cohomologically Induced Modules

Part of the Mathematics: Theory & Applications book series (MTA)


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, LK)-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:
  1. nonzero only in the middle degree S, and moreover RS (Z) ≔ Ls(Z);

  2. irreducible if Z is irreducible;

  3. unitary if Z is unitary.



Spectral Sequence Natural Isomorphism Cartan Subalgebra Adjoint Action Good Range 
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© Birkhäuser Boston 2006

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