A duality theorem for extensions of induced highest weight modules

David H. Collingwood and Brad Shelton

Vol. 146 (1990), No. 2, 227–237

DOI: 10.2140/pjm.1990.146.227

Abstract

We begin by recalling that homogeneous differential operators between smooth vector bundles over a real flag manifold correspond to the intertwining maps between algebraically induced highest weight modules. Within this framework we prove a duality theorem for extensions of induced highest weight modules. In particular, this leads to a duality theory for the nilpotent cohomology of any generalized Verma module.

Mathematical Subject Classification 2000

Primary: 22E47

Milestones

Received: 12 December 1988

Revised: 11 July 1989

Published: 1 December 1990