Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

✍ Scribed by Andrzej Daszkiewicz; Witold Kraśkiewicz; Tomasz Przebinda

• Book ID: 111487651
• Publisher: SP Versita
• Year: 2005
• Tongue: English
• Weight: 474 KB
• Volume: 3
• Category: Article
• ISSN: 1895-1074
• DOI: 10.2478/bf02475917

✦ Synopsis

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.