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 | References | Similar Articles | Additional Information

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

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

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.