### Abstract

We consider a reductive dual pair (G, G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K′_{ℂ}-orbits, where K′ is a maximal compact subgroup of G′ and we describe the precise K _{ℂ}-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K _{ℂ}-orbits obtained in this way. We also give integral formulas for their degrees.

Original language | English |
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Pages (from-to) | 2713-2734 |

Number of pages | 22 |

Journal | Transactions of the American Mathematical Society |

Volume | 358 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*358*(6), 2713-2734. https://doi.org/10.1090/S0002-9947-05-03826-2

**Theta lifting of nilpotent orbits for symmetric pairs.** / Nishiyama, Kyo; Ochiai, Hiroyuki; Zhu, Chen Bo.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 358, no. 6, pp. 2713-2734. https://doi.org/10.1090/S0002-9947-05-03826-2

}

TY - JOUR

T1 - Theta lifting of nilpotent orbits for symmetric pairs

AU - Nishiyama, Kyo

AU - Ochiai, Hiroyuki

AU - Zhu, Chen Bo

PY - 2006/6/1

Y1 - 2006/6/1

N2 - We consider a reductive dual pair (G, G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K′ℂ-orbits, where K′ is a maximal compact subgroup of G′ and we describe the precise K ℂ-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K ℂ-orbits obtained in this way. We also give integral formulas for their degrees.

AB - We consider a reductive dual pair (G, G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K′ℂ-orbits, where K′ is a maximal compact subgroup of G′ and we describe the precise K ℂ-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K ℂ-orbits obtained in this way. We also give integral formulas for their degrees.

UR - http://www.scopus.com/inward/record.url?scp=33744765489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744765489&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-05-03826-2

DO - 10.1090/S0002-9947-05-03826-2

M3 - Article

AN - SCOPUS:33744765489

VL - 358

SP - 2713

EP - 2734

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -