Actions of Maximal Tori on Homogeneous Spaces

George Tomanov ()
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George Tomanov: Université Claude Bernard - Lyon 1, Institut Girard Desargues, UMR 5028 - Mathématiques

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 407-424 from Springer

Abstract: Abstract We consider the natural action of maximal tori of real algebraic groups on homogeneous spaces defined as quotients of the real algebraic groups by their arithmetic subgroups. The study of the orbit closures in this context is closely related to important problems from number theory, in particular, with the notable Littlewood conjecture. We mainly concentrate on two classes of orbits: 1) relatively compact and, 2) divergent orbits. In the former case we generalize recent results of Lindenstrauss and Weiss. In the latter one we announce new results (due to Margulis, Weiss and the author) which show that the divergent and, more generally, the closed orbits are always standard.

Keywords: Homogeneous Space; Algebraic Group; Division Algebra; Orbit Closure; Unipotent Radical (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_22

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DOI: 10.1007/978-3-662-04743-9_22

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