Theta Lifting of Nilpotent Orbits for Symmetric Pairs
نویسندگان
چکیده
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 KC-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 KC-orbits obtained in this way. We also give integral formulas for their degrees.
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