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Local geometry of orbits for an ordinary classical lie supergroup

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Przebinda T.

Open Mathematics

2006

tom 4

nr 3

449-506

In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.

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

100%

Daszkiewicz A., Kraśkiewicz W., Przebinda T.

Open Mathematics

2005

tom 3

nr 3

430-474

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.

Ograniczanie wyników

2 Open Mathematics

2 Przebinda T.

1 Daszkiewicz A.

1 Kraśkiewicz W.

1 2006

1 2005

Wyniki wyszukiwania

Local geometry of orbits for an ordinary classical lie supergroup

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