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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Spherical nilpotent orbits and the Kostant-Sekiguchi correspondence


Author: Donald R. King
Journal: Trans. Amer. Math. Soc. 354 (2002), 4909-4920
MSC (2000): Primary 22E46; Secondary 14R20, 53D20.
DOI: https://doi.org/10.1090/S0002-9947-02-03089-1
Published electronically: August 1, 2002
MathSciNet review: 1926842
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Abstract: Let $G$ be a connected, linear semisimple Lie group with Lie algebra $\mathfrak g$, and let ${K_{{}_{\mathbf C}}}~\rightarrow~{\operatorname{Aut} (\mathfrak p_{{}_{\mathbf C}})}$ be the complexified isotropy representation at the identity coset of the corresponding symmetric space. The Kostant-Sekiguchi correspondence is a bijection between the nilpotent $K_{{}_{\mathbf C}}$-orbits in $\mathfrak p_{{}_{\mathbf C}}$ and the nilpotent $G$-orbits in $\mathfrak g$. We show that this correspondence associates each spherical nilpotent $K_{{}_{\mathbf C}}$-orbit to a nilpotent $G$-orbit that is multiplicity free as a Hamiltonian $K$-space. The converse also holds.


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Additional Information

Donald R. King
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: donking@neu.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03089-1
Received by editor(s): February 7, 2001
Received by editor(s) in revised form: April 16, 2002
Published electronically: August 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society