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arXiv: 0812.4275

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Annales de l'Institut Fourier 61, 2 (2011) 417-451

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v1 (2008-12-22)

v2 (2010-06-30)

Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.

Karin Baur 1, Anne Moreau (  Corresponding author ) 2

(2011)

We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo, Khalgui and Torasso. In this paper, we investigate the quasi-reductivity of biparabolic subalgebras of reductive Lie algebras. Biparabolic (or seaweed) subalgebras are the intersection of two parabolic subalgebras whose sum is the total Lie algebra. As a main result, we complete the classification of quasi-reductive parabolic subalgebras of reductive Lie algebras by considering the exceptional cases.

1:	ETH Zürich D-MATH (ETH)
	ETH - D-MATH
2:	Laboratoire de Mathématiques et Applications (LMA-Poitiers)
	CNRS : UMR6086 – Université de Poitiers

Subject

:

Mathematics/Representation Theory

Keyword(s): reductive Lie algebras – quasi-reductive Lie algebras – index – biparabolic Lie algebras – seaweed algebras – regular linear forms

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From: Anne Moreau <>

Submitted on: Wednesday, 30 June 2010 15:04:18

Updated on: Thursday, 13 October 2011 11:08:24