| Publication type: |
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Article in peer-reviewed journal |
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| Subject: |
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Mathematics/Representation Theory
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| Title: |
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Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras. |
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| Author(s): |
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Karin Baur 1, Anne Moreau ( ) 2 |
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| Laboratory: |
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| Abstract: |
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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 The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo, Khalgui and Torasso.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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| Fulltext language: |
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English |
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| Journal: |
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Annales de l'Institut Fourier |
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| Audience: |
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international |
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| Publication date: |
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2011 |
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| Volume: |
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61 |
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| Issue: |
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2 |
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| Page, identifiant, ...: |
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417-451 |
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| Keyword(s): |
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reductive Lie algebras – quasi-reductive Lie algebras – index – biparabolic Lie algebras – seaweed algebras – regular linear forms |
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| Classification: |
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17B20, 17B45, 22E60 |
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| Comment: |
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20 pages |
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