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ISSN 1088-6850(e) ISSN 0002-9947(p)

Theta lifting of nilpotent orbits for symmetric pairs

Authors: Kyo Nishiyama, Hiroyuki Ochiai and Chen-bo Zhu
Journal: Trans. Amer. Math. Soc. 358 (2006), 2713-2734
MSC (2000): Primary 22E46, 11F27
Posted: December 20, 2005
MathSciNet review: 2204053
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Abstract: We consider a reductive dual pair in the stable range with the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent $K'_{\mathbb{C}}$ -orbits, where is a maximal compact subgroup of and we describe the precise $K_{\mathbb{C}}$ -module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair . As an application, we prove sphericality and normality of the closure of certain nilpotent $K_{\mathbb{C}}$ -orbits obtained in this way. We also give integral formulas for their degrees.

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