Theta lifting of nilpotent orbits for symmetric pairs

Kyo Nishiyama, Hiroyuki Ochiai, Chen Bo Zhu

Research output: Contribution to journalArticle

8 Citations (Scopus)

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′-orbits, where K′ is a maximal compact subgroup of G′ and we describe the precise K -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 -orbits obtained in this way. We also give integral formulas for their degrees.

Original languageEnglish
Pages (from-to)2713-2734
Number of pages22
JournalTransactions of the American Mathematical Society
Volume358
Issue number6
DOIs
Publication statusPublished - Jun 1 2006

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Nilpotent Orbits
Closure
Orbits
Orbit
Integral Formula
Normality
Subgroup
Ring
Module
Range of data

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Transactions of the American Mathematical Society, Vol. 358, No. 6, 01.06.2006, p. 2713-2734.

Research output: Contribution to journalArticle

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