Nice parabolic subalgebras of reductive Lie algebras
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- by Karin Baur and Nolan Wallach
- Represent. Theory 9 (2005), 1-29
- DOI: https://doi.org/10.1090/S1088-4165-05-00262-1
- Published electronically: January 10, 2005
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Erratum: Represent. Theory 9 (2005), 267-267.
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).References
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Bibliographic Information
- Karin Baur
- Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
- MR Author ID: 724373
- ORCID: 0000-0002-7665-476X
- Email: kbaur@math.ucsd.edu
- Nolan Wallach
- Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
- MR Author ID: 180225
- Email: nwallach@math.ucsd.edu
- 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 - © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 9 (2005), 1-29
- MSC (2000): Primary 17B45
- DOI: https://doi.org/10.1090/S1088-4165-05-00262-1
- MathSciNet review: 2123123