The closure diagram for nilpotent orbits of the split real form of E8 |
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Authors: | Đoković Dragomir Ž |
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Institution: | (1) Department of Pure Mathematics, University of Waterloo, N2L 3G1 Waterloo, Ontario, Canada |
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Abstract: | Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. |
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Keywords: | Exceptional Lie groups adjoint action closures of nilpotent orbits normal triples Kostant-Sekiguchi bijection prehomogeneous vector spaces |
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