Nice Parabolic Subalgebras of Reductive Lie Algebras

Details Nice Parabolic Subalgebras of Reductive Lie Algebras Nice Parabolic Subalgebras of Reductive Lie Algebras

2004-09-17

arxiv.org/abs/math/0409295v2

Represent. Theory 9 (2005), 1-29

Mathematics

Representation Theory

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

Scientific paper

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).

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