Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements |
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Authors: | Daszkiewicz Andrzej Kraśkiewicz Witold Przebinda Tomasz |
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Institution: | (1) Faculty of Mathematics, Nicholas Copernicus University, Chopina 12, 87-100 Toruń, Poland;(2) Department of Mathematics, University of Oklahoma, 73019 Norman, OK, USA |
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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. |
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Keywords: | Dual pairs nilpotent orbits Lie color algebras Kostant-Sekiguchi correspondence |
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