Question

I am now learning induction problems in representation theory. I know David Vogan's book cohomological induction and unitary representation theory might be good references,but it is too thick.

I wonder whether there is some good and detailed notes on using derived functor to construct irreducible representations. It seems that Zuckermann ever gave a series of talks at Yale to introduce this method, but unfortunately, it was not published.

It seems that this method was motivated by Schmid's phd thesis. But I did not have schmid's phd thesis either.

All the related comments are welcomed

Answer 1

You might look at Vogan's orange book "Unitary Representations of Reductive Lie Groups," which is a much thinner book, or (thinner yet) chapters 5-6 of "Dirac Operators in Representation Theory," by Jing-Song Huang and Pavle Pandzic. These both have descriptions of cohomological induction, though off the top of my head I forget what information they include specifically about irreducible representations.