Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements
Andrzej Daszkiewicz ; Witold Kraśkiewicz ; Tomasz Przebinda
Open Mathematics, Tome 3 (2005), p. 430-474 / Harvested from The Polish Digital Mathematics Library
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We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268787 
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     title = {Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {430-474},
     zbl = {1107.22007},
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Andrzej Daszkiewicz; Witold Kraśkiewicz; Tomasz Przebinda. Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements. Open Mathematics, Tome 3 (2005) pp. 430-474. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475917/

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