Kyo Nishiyama, Hiroyuki Ochiai, Chen-bo Zhu
Published 2003-12-25Version 1
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.
Comments: 26 pages
Journal: Trans. Amer. Math. Soc., 358(2006), no. 6, 2713--2734
On the branching rules for Klein four symmetric pairs
A criterion for discrete branching laws for Klein four symmetric pairs and its application to $E_{6(-14)}$
Branching of unitary $\operatorname{O}(1,n+1)$-representations with non-trivial $(\mathfrak{g},K)$-cohomology
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