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

Abstract

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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.

How to cite

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Andrzej 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 -

References

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