Theta lifting of nilpotent orbits for symmetric pairs

Details Theta lifting of nilpotent orbits for symmetric pairs Theta lifting of nilpotent orbits for symmetric pairs

2003-12-25

arxiv.org/abs/math/0312453v1

Trans. Amer. Math. Soc., 358(2006), no. 6, 2713--2734

Mathematics

Representation Theory

26 pages

Scientific paper

10.1090/S0002-9947-05-03826-2

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.

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