Loewy series and simple projective modules in the category 𝒪_S

Ronald Scott Irving and Brad Shelton

Vol. 132 (1988), No. 2, 319–342

DOI: 10.2140/pjm.1988.132.319

Abstract

Results are obtained on the Loewy length and Loewy series of generalized Verma modules and projective modules in certain categories 𝒪_S of modules over a complex, semisimple Lie algebra. The results obtained rely on a study of the behavior of Loewy series under translation functors and on the existence of simple projective modules in suitable blocks of 𝒪_S. An example is given of two generalized Verma modules such that the space of 𝒪_S-homomorphisms from the first to the second is two-dimensional.

Mathematical Subject Classification 2000

Primary: 17B10

Milestones

Received: 14 October 1986

Published: 1 April 1988