Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces

• 成果类型: Article
• 署名作者: Einsiedler, M.; Margulis, G.; Venkatesh, A.
• 署名单位: University System of Ohio; Ohio State University; Yale University; Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0177-7
• 发表日期: 2009
• 页码: 137-212
• 关键词: prehomogeneous vector-spaces; unipotent flows; matrix coefficients; unitary representations; asymptotic-behavior; invariant-measures; measure rigidity; quadratic-forms; horocycle flow; ergodic-theory

摘要

We prove effective equidistribution, with polynomial rate, for large closed orbits of semisimple groups on homogeneous spaces, under certain technical restrictions (notably, the acting group should have finite centralizer in the ambient group). The proofs make extensive use of spectral gaps, and also of a closing lemma for such actions.