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2003 | 1 | 4 | 573-643
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $$\overline {\mathcal{O}_l^i } \cap \overline {\mathcal{O}_l^j } $$ .
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
4
Strony
573-643
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Twórcy
Bibliografia
  • [1] D. Barbasch and M.R. Sepanski: “Closure ordering and the Kostant-Sekiguchi correspondence”, Proc. Amer. Math. Soc., Vol. 126, (1998), pp. 311–317. http://dx.doi.org/10.1090/S0002-9939-98-04090-8
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  • [8] D.Ž. Đoković: “Explicit Cayley triples in real forms of G 2, F 4, and E 6”, Pacific. J. Math., Vol. 184, (1998), pp. 231–255.
  • [9] D.Ž. Đoković: “Explicit Cayley triples in real forms of E 8”, Pacific J. Math.”, Vol. 194, (2000), pp. 57–82. http://dx.doi.org/10.2140/pjm.2000.194.57
  • [10] D.Ž. Đoković: “The closure diagrams for nilpotent orbits of real forms of F 4 and G 2”, J. Lie Theory, Vol. 10, (2000), pp. 491–510.
  • [11] D.Ž. Đoković: “The closure diagrams for nilpotent orbits of real forms of E 6”, J. Lie Theory, 11, (2001), pp. 381–413.
  • [12] D.Ž. Đoković: “The closure diagrams for nilpotent orbits of the real forms EVI and EVII of E 7”, Represent. Theory, Vol. 5, (2001), pp. 17–42. http://dx.doi.org/10.1090/S1088-4165-01-00112-1
  • [13] D.Ž. Đoković: “The closure diagram for nilpotent orbits of the split real forms of E 7”, Represent. Theory, Vol. 5, (2001), pp. 284–316. http://dx.doi.org/10.1090/S1088-4165-01-00124-8
  • [14] D.Ž. Đoković: “The closure diagram for nilpotent orbits of the real form EIX of E 8”, Asian J. Math., Vol. 5, (2001), pp. 561–584.
  • [15] K. Mizuno: “The conjugate classes of unipotent elements of the Chevalley groups E 7 and E 8”, Tokyo J. Math., Vol. 3, (1980), pp. 391–461. http://dx.doi.org/10.3836/tjm/1270473003
  • [16] A. Mortajine: Classification des espaces préhomogènes de type parabolique réguliers et de leurs invariants relatifs, Hermann, Paris, 1991.
  • [17] M. Sato and T. Kimura: “A classification of irreducible prehomogeneous vector spaces and their relative invariants”, Nagoya Math. J., Vol. 65, (1977), pp. 1–155.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475183
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