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Representation Theory

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The closure diagrams for nilpotent orbits of the real forms EVI and EVII of $\mathbf{E_7}$

Author: Dragomir Z. Dokovic
Journal: Represent. Theory 5 (2001), 17-42
MSC (2000): Primary 05B15, 05B20; Secondary 05B05
Published electronically: February 2, 2001
Correction: Theory 5 (2001), 503-503
MathSciNet review: 1826427
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Let $\mathcal{O}_1$ and $\mathcal{O}_2$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write $\mathcal{O}_1\geq\mathcal{O}_2$ if $\mathcal{O}_2$ is contained in the closure of $\mathcal{O}_1.$ This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the two noncompact nonsplit real forms of the simple complex Lie algebra $E_7.$

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Additional Information

Dragomir Z. Dokovic
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Received by editor(s): August 15, 2000
Received by editor(s) in revised form: December 6, 2000
Published electronically: February 2, 2001
Additional Notes: Supported in part by the NSERC Grant A-5285.
Article copyright: © Copyright 2001 American Mathematical Society