Spherical Nilpotent Orbits and the Kostant-sekiguchi Correspondence

  title={Spherical Nilpotent Orbits and the Kostant-sekiguchi Correspondence},
  author={Donald P. King},
Let G be a connected, linear semisimple Lie group with Lie algebra g, and let KC → Aut(pC ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. The Kostant-Sekiguchi correspondence is a bijection between the nilpotent KC -orbits in pC and the nilpotent G-orbits in g. We show that this correspondence associates each spherical nilpotent KC -orbit to a nilpotent G-orbit that is multiplicity free as a Hamiltonian K-space. The converse also holds. 

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