Theta lifting of nilpotent orbits for symmetric pairs

Kyo Nishiyama, Hiroyuki Ochiai, Chen Bo Zhu

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9 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 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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