The Nevo–Zimmer intermediate factor theorem over local fields

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• 作者：Arie Levit
• 关键词：Invariant random subgroups ; Stuck–Zimmer theorem ; Intermediate factor theorem ; Measure algebras ; Probability measure preserving actions ; Linear algebraic groups over a local field
• 刊名：Geometriae Dedicata
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：186
• 期：1
• 页码：149-171
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9168
• 卷排序：186

文摘

The Nevo–Zimmer theorem classifies the possible intermediate G-factors Y in , where G is a higher rank semisimple Lie group, P a minimal parabolic and X an irreducible G-space with an invariant probability measure. An important corollary is the Stuck–Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set. We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields.