# The closure diagram for nilpotent orbits of the split real form of E8

Open Mathematics (2003)

- Volume: 1, Issue: 4, page 573-643
- ISSN: 2391-5455

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topDragomir Đoković. "The closure diagram for nilpotent orbits of the split real form of E8." Open Mathematics 1.4 (2003): 573-643. <http://eudml.org/doc/268838>.

@article{DragomirĐoković2003,

abstract = {Let \[\mathcal \{O\}\_1 \]
and \[\mathcal \{O\}\_2 \]
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write \[\mathcal \{O\}\_1 \]
≥ \[\mathcal \{O\}\_2 \]
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 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 \[\partial \mathcal \{O\}\_1^i \]
and of the intersections \[\overline\{\mathcal \{O\}\_l^i \} \cap \overline\{\mathcal \{O\}\_l^j \} \]
.},

author = {Dragomir Đoković},

journal = {Open Mathematics},

keywords = {17B25; 17B45},

language = {eng},

number = {4},

pages = {573-643},

title = {The closure diagram for nilpotent orbits of the split real form of E8},

url = {http://eudml.org/doc/268838},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Dragomir Đoković

TI - The closure diagram for nilpotent orbits of the split real form of E8

JO - Open Mathematics

PY - 2003

VL - 1

IS - 4

SP - 573

EP - 643

AB - Let \[\mathcal {O}_1 \]
and \[\mathcal {O}_2 \]
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write \[\mathcal {O}_1 \]
≥ \[\mathcal {O}_2 \]
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 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 \[\partial \mathcal {O}_1^i \]
and of the intersections \[\overline{\mathcal {O}_l^i } \cap \overline{\mathcal {O}_l^j } \]
.

LA - eng

KW - 17B25; 17B45

UR - http://eudml.org/doc/268838

ER -

## References

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