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ISSN 1088-4165

 

 

Nice parabolic subalgebras of reductive Lie algebras


Authors: Karin Baur and Nolan Wallach
Journal: Represent. Theory 9 (2005), 1-29
MSC (2000): Primary 17B45
DOI: https://doi.org/10.1090/S1088-4165-05-00262-1
Published electronically: January 10, 2005
Erratum: Represent. Theory 9 (2005), 267-267.
MathSciNet review: 2123123
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Abstract: This paper gives a classification of parabolic subalgebras of simple Lie algebras over ${\mathbb C}$ 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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Additional Information

Karin Baur
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
Email: kbaur@math.ucsd.edu

Nolan Wallach
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
Email: nwallach@math.ucsd.edu

DOI: https://doi.org/10.1090/S1088-4165-05-00262-1
Received by editor(s): October 5, 2004
Received by editor(s) in revised form: November 1, 2004
Published electronically: January 10, 2005
Additional Notes: First named author supported by the Swiss National Science Foundation
Second named author partially supported by an NSF summer grant
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.