Theta lifting of nilpotent orbits for symmetric pairs

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.

26 pages

Cited by in corpus (8)

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• Small spherical nilpotent orbits and K-types of Harish Chandra modules
• Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian
• Associated cycles of local theta lifts of unitary characters and unitary lowest weight modules
• Projective cases for the restriction of the oscillator representation to dual pairs of type I
• Local theta lifting of generalized Whittaker models associated to nilpotent orbits