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

Dragomir Đoković

Open Mathematics (2003)

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

Abstract

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Let 𝒪 1 and 𝒪 2 be adjoint nilpotent orbits in a real semisimple Lie algebra. Write 𝒪 1 ≥ 𝒪 2 if 𝒪 2 is contained in the closure of 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 ∂ 𝒪 1 i and of the intersections 𝒪 l i ¯ ∩ 𝒪 l j ¯ .

How to cite

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Dragomir 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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