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

• Autorzy: Andrzej Daszkiewicz , Witold Kraśkiewicz , Tomasz Przebinda
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Dual pairs; nilpotent orbits; Lie color algebras; Kostant-Sekiguchi correspondence; 20G05; 17B75; 22E45

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 3
• Strony: 430-474

Daty

wydano

2005-09-01

online

2005-09-01

Twórcy

autor

Andrzej Daszkiewicz

• Nicholas Copernicus University

autor

Witold Kraśkiewicz

• Nicholas Copernicus University

autor

Tomasz Przebinda

• University of Oklahoma

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475917