Theta lifting of nilpotent orbits for symmetric pairs
Representation Theory
2010-12-16 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0312453,
title = {Theta lifting of nilpotent orbits for symmetric pairs},
author = {Kyo Nishiyama and Hiroyuki Ochiai and Chen-bo Zhu},
journal= {arXiv preprint arXiv:math/0312453},
year = {2010}
}
Comments
26 pages