Category \({\mathcal O}'\), \({\mathfrak n}\)-homology and the reducibility of generalized principal series representations (Q794782)

Let G be a connected semisimple real matrix group. Using Verma modules, the Bernstein-Gelfand-Gelfand theorem, the Jacquet functor and elegant connections between the asymptotic behavior of matrix coefficients, characters, \({\mathfrak n}\)-homology and interwining operators, the author gives a new proof of reducibility criteria for generalized principal series representations of G.