Theta lifting of nilpotent orbits for symmetric pairs

  title={Theta lifting of nilpotent orbits for symmetric pairs},
  author={Kyo Nishiyama and Hiroyuki Ochiai and Chen-bo Zhu},
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… CONTINUE READING

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