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I have split off a brief entry Zuckerman induction from cohomological induction (since the basic version is not necessarily derived).
This is not appropriate in my opinion. Most often by "Zuckerman functor" one means the derived version, so one expects to have the entry Zuckerman functor to be what is this by the default. I think separating the two small and naturally almost equivalent entries is not beneficial. Better to have one more comprehensive entry with redirect, I think. Though I do not feel particularly strong about it.
It would help me if you give pointers to the literature that you are thinking of. What I put into “Zuckerman induction” is exactly what that article says which you pointed to last time and which is pointed to in the entry.
I do not know the literature in this area, except those I mentioned in the entry. Almost all I heard about this is from many seminars I attended in representation theory and some discussions. I pointed to you a modern article clearing out the issue about derived and sheaf theoretic origin of the math behind Zuckerman functors, what you asked. This is not the most mainstream, traditional article explaining conventional wisdom and terminology, but rather an attempt to modernize the subject in the sheaf theoretic, geometric and categorical direction you probably like. Though this is far not the main issue in this area.
There will be a representation theory conference in Dubrovnik next June, where main focus is precisely about this issues, if you are interested. Vogan, Pandžić, MIličić, Vilonen, Mirković will be among the speakers for sure, and in past they were sometimes inviting Zuckerman as well.
Okay, so I don’t know what you did in the seminar, but what I see is an article that defines Zuckerman induction the way I did in the entry and which does not mention the term “cohomological induction”. So it would seem inappropriate to have this definition only at “cohomological induction”.
But even if it were otherwise, I don’t think there is any harm done in having an entry with the specific title “Zuckerman induction”.
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