Cohomological induction is a derived functor version of induction functors in representation theory. As the elements in induced representations correspond to sections of certain equivariant bundles or sheaves, similarly the cohomological induction functors could be interpreted as higher cohomologies of certain equivariant sheaves.

In specific contexts, like real Lie groups, there are specifical versions like Zuckerman induction functors?; they are defined algebraically.

Dragan Miličić, Pavle Pandžić, Equivariant derived categories, Zuckerman functors and localization, from Geometry and Representation Theory of real and p-adic Lie Groups , J. Tirao, D. Vogan, J.A. Wolf, editors, Progress in Mathematics 158, Birkhäuser, Boston, 1997, 209-242, pdf

Toshiyuki Kobayashi, Branching problems of Zuckerman derived functor modules, arxiv/1104.4399

Greg J. Zuckerman, Construction of representations via derived functors, unpublished lecture series, Institute for Advanced Study, 1978.

Jia-jun Ma, Derived functor modules, dual pairs and $U(\mathfrak{g})^K$-actions, arxiv/1310.6378

Revised on July 18, 2014 03:15:08
by Anonymous Coward
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