nLab cohomological induction

Idea

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.

Related concepts

• Zuckerman induction

Literature

• A. Knapp, David A. Vogan, Cohomological induction and unitary representations, MR1330919
• wikipedia Zuckerman functor
• Pavle Pandžić, Zuckerman functors between equivariant derived categories, Trans. Amer. Math. Soc. 359 (2007), 2191-2220 MR2276617 pdf
• 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• Greg J. Zuckerman, Construction of representations via derived functors, unpublished lecture series, Institute for Advanced Study, 1978.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