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

Andrzej Daszkiewicz; Witold Kraśkiewicz; Tomasz Przebinda

Open Mathematics (2005)

- Volume: 3, Issue: 3, page 430-474
- ISSN: 2391-5455

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topAndrzej Daszkiewicz, Witold Kraśkiewicz, and Tomasz Przebinda. "Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements." Open Mathematics 3.3 (2005): 430-474. <http://eudml.org/doc/268787>.

@article{AndrzejDaszkiewicz2005,

abstract = {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.},

author = {Andrzej Daszkiewicz, Witold Kraśkiewicz, Tomasz Przebinda},

journal = {Open Mathematics},

keywords = {20G05; 17B75; 22E45},

language = {eng},

number = {3},

pages = {430-474},

title = {Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements},

url = {http://eudml.org/doc/268787},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Andrzej Daszkiewicz

AU - Witold Kraśkiewicz

AU - Tomasz Przebinda

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

JO - Open Mathematics

PY - 2005

VL - 3

IS - 3

SP - 430

EP - 474

AB - 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.

LA - eng

KW - 20G05; 17B75; 22E45

UR - http://eudml.org/doc/268787

ER -

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