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

Karin Baur; Anne Moreau

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arXiv · 0812.4275

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

Karin Baur·Anne Moreau

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Abstract

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 The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo, Khalgui and Torasso.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.

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BibTeX RIS

Karin Baur, Anne Moreau. 2010-06-30. Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras. https://arxiv.org/abs/0812.4275

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