Complexity of Nilpotent Orbits and the Kostant-sekiguchi Correspondence
نویسنده
چکیده
Let G be a connected linear semisimple Lie group with Lie algebra g, and let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that Ω is a nilpotent G-orbit in g and O is the nilpotent K C -orbit in p C associated to Ω by the Kostant-Sekiguchi correspondence. We show that the complexity of O as a K C variety measures the failure of the Poisson algebra of smooth K-invariant functions on Ω to be commutative.
منابع مشابه
Spherical Nilpotent Orbits and the Kostant-sekiguchi Correspondence
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 -orbi...
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