Intertwining differential operators and reducibility of generalized Verma modules (Q1318168)

This is an extension to vector bundles of \textit{B. Kostant}'s results on quasi-invariant differential operators for multiplier representations [Lect. Notes Math. 466, 101-128 (1975; Zbl 0372.22009)]. We define the matrix-valued intertwining differential operators and the leading weight vector spaces of generalized Verma modules and study their relationship. We show that the existence of non-trivial intertwining differential operators is equivalent to the reducibility of generalized Verma modules.