Nice parabolic subalgebras of reductive Lie algebras

Abstract

This paper gives a classification of parabolic subalgebras of simple Lie algebras over C \mathbb {C} that are complexifications of parabolic subalgebras of real forms for which Lynch’s vanishing theorem for generalized Whittaker modules is non-vacuous. The paper also describes normal forms for the admissible characters in the sense of Lynch (at least in the quasi-split cases) and analyzes the important special case when the parabolic is defined by an even embedded TDS (three-dimensional simple Lie algebra).