Transactions of the American Mathematical Society

Author(s): Kyo Nishiyama; Hiroyuki Ochiai; Chen-bo Zhu
Journal: Trans. Amer. Math. Soc. 358 (2006), 2713-2734.
MSC (2000): Primary 22E46, 11F27
Posted: December 20, 2005
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 22E46, 11F27

Kyo Nishiyama
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan
Email: kyo@math.kyoto-u.ac.jp

Hiroyuki Ochiai
Affiliation: Department of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
Email: ochiai@math.nagoya-u.ac.jp

Chen-bo Zhu
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Email: matzhucb@nus.edu.sg

DOI: 10.1090/S0002-9947-05-03826-2
PII: S 0002-9947(05)03826-2
Keywords: Reductive dual pair, theta lifting, nilpotent orbits, harmonic polynomial, invariant theory
Received by editor(s): December 18, 2003,
Received by editor(s) in revised form: August 14, 2004
Posted: December 20, 2005
Dedicated: Dedicated to Roger Howe on his sixtieth birthday
Copyright of article: Copyright 2005, American Mathematical Society

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