Nice Parabolic Subalgebras of Reductive Lie Algebras

Abstract

This paper gives a classification of parabolic subalgebras of simple Lie algebras over $\CC$ 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).

30 pages. Corrected version of statement 1.4 and of the list for E8

References in corpus (2)

• Good Gradings of Simple Lie Algebras
• A normal form for admissible characters in the sense of Lynch